Weisstein, Eric W. " Strongly Regular Graph ". or, E = (N*K)/2. Journal of Graph … In the mathematical field of graph theory, the Meringer graph is a 5-regular undirected graph with 30 vertices and 75 edges named after Markus Meringer. A typical problem in optimal design theory is finding an experimental design that is optimal with respect to some criteria in a class of designs. Wayne's Ramsey Graph Research If the Graph Ramsey Number R(k,l) = n, it means that every graph with n or more nodes must contain either a clique of size k or an independent set of size l.Ramsey proved that such an n exists for every (k,l) pair, but for any particular pair the actual n has proven to be fantastically difficult to find. In this paper we apply Kadhe and Calderbank's definition of LRCs from convex polyhedra and planar graphs \cite{KAD} to analyze the codes resulting from 3-connected regular and almost regular planar graphs. The characteristic polynomial of the Meringer graph is, 10.1002/(SICI)1097-0118(199902)30:2<137::AID-JGT7>3.0.CO;2-G, https://en.wikipedia.org/w/index.php?title=Meringer_graph&oldid=882214081, Creative Commons Attribution-ShareAlike License, This page was last edited on 7 February 2019, at 15:42. ... Meringer graph.svg 420 × 420; 10 KB. ... sequence from regular graphs as the most simple graphs [11]. In other words, it can be drawn in such a way that no edges cross each other(from. In the mathematical field of graph theory, the Meringer graph is a 5-regular undirected graph with 30 vertices and 75 edges named after Markus Meringer.It is one of the four (5,5)-cage graphs, the others being the Foster cage, the Robertson–Wegner graph, and the Wong graph. regular graph, not necessarily connected.. A. Hulpke (1996) computed transitive groups up to degree 30. Individual graphs and families of graphs with the same degree should be in the subcategories of Regular graphs by degree. The implementation is attached at di_gen.c. House of Graphs, Cubic graphs. MathWorld (英語). H. Gropp, Enumeration of regular graphs 100 years ago, Discrete Math., 101 (1992), 73-85. Then, the graph B q (u) is (q − u)-regular of order 2 (q 2 − q u) and the graph B q (S, T, u) is bi-regular with degrees (q − u − 1, q − u) and order 2 (q 2 − q u) − | S | − | T |. In the mathematical field of graph theory, the Meringer graph is a 5-regular undirected graph with 30 vertices and 75 edges named after Markus Meringer.[1][2]. Referred to the algorithm M. Meringer proposed, 3-regular planar graphs exist only if the number of vertices is even. This paper. GenReg software and data by Markus Meringer. Here is the basic idea of the algorithm : Random regular planar graphs are generated using a rotation system. READ PAPER. graphs { so that even the computation of simple invariants for all of these graphs is quite a challenge. Biggs: Algebraic Graph Theory. Rücker and G. Tinhofer, Algebraic Combinatorics [broken link] This collection contains all connected regular graphs of girth 3 up to the order 12, of girth 4 up to the order 16, and of girth 5 up to the order 23 (including graphs of girth 6). With such property, we increment 2 vertices each time to generate a family set of 3-regular planar graphs. 542-548 Mar/Apr. Run the executable file di_gen.exe followed by two arguments: min_n and max_n. GenReg software and data by Markus Meringer. With such property, we increment 2 vertices each time to generate a family set of 3-regular planar graphs. Download Full PDF Package. These graphs are all three-colorable. Adequate graph sizes for testing are between 10 ... Markus Meringer. The construction of complete lists of regular graphs up to isomorphism is one of the oldest problems in constructive combinatorics. DIMACS Series in Discrete Mathematics and Theoretical Computer Science 28, 113-122, 1997. ‪German Aerospace Center (DLR)‬ - ‪Cited by 2,337‬ - ‪Mathematics‬ - ‪Computer Science‬ - ‪Chemistry‬ - ‪Astrobiology‬ - ‪Spectrometry‬ Regular graphs of degree at most 2 are easy to classify: A 0-regular graph consists of disconnected vertices, a 1-regular graph consists of disconnected edges, and a 2-regular graph consists of a disjoint union of cycles A 3. " Regular Graph ". MathWorld (英語). T. Grüner, R. Laue, M. Meringer: Algorithms for Group Actions: Homomorphism Principle and Orderly Generation Applied to Graphs. This required a decomposition strategy different from that of DENDRAL, allowing to iterate the decomp osition in an un- MathWorld (angleščina). Meringer [4] proposed a practical method to construct regular graphs without pairwise isomorphism checking but with a fast test for canonicity. The smallest graphs that are regular but not strongly regular are the cycle graph and the circulant graph on 6 vertices. Robertson–Wegner graph.svg 420 × 420; 8 KB. It has chromatic number 3, diameter 3, and is 5-vertex-connected. A 0-regular graph is an empty graph, a 1-regular graph consists of disconnected edges, and a two-regular graph consists of one or more (disconnected) cycles. Captions. " Regular Graph ". On the other hand, random regular graphs are easy to construct and maintain, and provide good properties with high probability, but without strict guarantees. The most popular criteria include the A- and D-criteria. Summary [] Regular Graphs. <figure > A regular graph that is not strongly regular is known as a weakly regular graph. "Strongly Regular Graph". " Regular Graph ". 14-15). Most commonly, "cubic graphs" is used to mean "connected cubic graphs." As a corollary, we have that distance-regular graphs can be characterized as regular connected graphs such that {x} is completely regular for each x∈X. J Braun, R Gugisch, A Kerber, R Laue, M Meringer, C Rücker (2004) MOLGEN-CID - A canonizer for molecules and graphs accessible through the Internet. • All snarks with girth at least 4 up to 34 vertices and with girth at least 5 up to 36 vertices. A short summary of this paper. We develop regular product flyers without our logo, with space for the distributor’s stamp. Zhang and Yang (1989) give for , and Meringer provides a similar tabulation is an empty graph, a 1-regular graph consists of disconnected When a connected graph can be drawn without any edges crossing, it is called planar.When a planar graph is drawn in this way, it divides the plane into regions called faces.. A006821/M3168, A006822/M3579, Some regular graphs of degree … MathWorld (英語). In this paper, we introduce a new class of graphs that we call r 3 ( resilient random regular ) graphs and present a technique to create and maintain r 3 graphs. We iterates this process and create a family of 3-regular planar graphs. Subcategories. Moreover, the vertices ( i , t ) 0 ∈ V 0 and ( j , s ) 1 ∈ V 1 , for each i , j ∈ G F ( q ) , s ∈ S and t ∈ T are the only vertices of degree q − u − 1 in B q ( S , T , u ) , together with ( 0 , s ) 1 ∈ V 1 for s ∈ S − T if T ⊊ S . (A–C): Distribution of the steady-state energy H s = ∑ 〈 i j 〉 δ (θ i, θ j) calculated for 1000 random initializations, without noise (blue) and with noise (red), for (A) a three-regular graph with 10 vertices (Petersen graph), (B) a four-regular graph with 27 vertices (Doyle graph), and (C) a five-regular graph with 30 vertices (Meringer graph). Biggs: Algebraic Graph Theory. The method is based on orderly generation refined by criteria to avoid isomorphism checking and combined with a fast test for canonicity. (ISBN: 0-412-04131-6) Gr ¨ uner, M. Meringer, A. Kerb er. Generation of regular graphs. Bollobas: Modern Graph Theory. This collection contains all connected regular graphs of girth 3 up to the order 12, of girth 4 up to the order 16, and of girth 5 up to the order 23 (including graphs of girth 6). A rotation system means that the graph is represented in an adjacency list that has the clockwise order for the neighbours of each vertex. A strongly regular graph is a regular graph where every adjacent pair of vertices has the same number l of neighbors in common, and every non-adjacent pair of vertices has the same number n of neighbors in common. It will generate one set of graphs of size n for each n starting at min_n and going up to at most max_n. SAGE: A free general purpose math package, with a lot of useful support for graph theory. We know exactly how to help our business partners with it. MathWorld (英語). MOLGEN-CID - A Canonizer for Molecules and Graphs Accessible through the Internet. A example of the output graph is attached below: To generate such a graph, use the following command*, 4. Marketing is an important part of business. It also provides access to many other useful packages. Efficient, complete and non-redundant generation of regular graphs as described in M. Meringer: Fast Generation of Regular Graphs and Construction of Cages. Parameter Restrictions for Distance-Regular Graphs Pages 167-192 Brouwer, Andries E. (et al.) Markus Meringer's regular graphs. Adv. Download PDF. Meringer [14] proposed a Efficient, complete and non-redundant generation of regular graphs as described in M. Meringer: Fast Generation of Regular Graphs and Construction of Cages. Nash-Williams, Crispin (1969), “Valency Sequences which force graphs to We generate all the 3-regular planar graphs based on K4. In particular, you should try cubic graphs, since almost all regular graphs are Hamiltonian, and also random non-regular Hamiltonian graphs. Download. Math. Download GenReg for free. 4-regular simple graphs: A006820 (connected), A033483 (disconnected), this sequence (not necessarily connected). The implementation allows computing even large classes of graphs, like construction of the 4‐regular graphs on 18 vertices and, for the first time, the 5‐regular graphs on 16 vertices. The first interesting case is therefore 3-regular graphs, which are called cubic graphs (Harary 1994, pp. Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g. M. Klin, M. Rücker, Ch. We create websites such as pessar.pl, visited by more than 10,000 customers, where we … All graphs registered as interesting in the database. Bannai, Eiichi, Bannai, Etsuko: On ... Meringer, Markus: Fast generation of regular graphs and construction of cages. ), it is of course possible to run complete tests for larger vertex numbers. Journal of Graph Theory 30, 137-146, 1999. J. Graph … Related Texts Reinhard Diestel: Graph Theory (Springer 1997). Markus Meringer's regular graphs. Generation of regular graphs. Weisstein, Eric W. " Strongly Regular Graph ". Nash-Williams, Crispin (1969), “Valency Sequences which force graphs to Related Texts Reinhard Diestel: Graph Theory (Springer 1997). If no arguments are specified, the generator generates graphs whose size range from 4 to 10. Markus Meringer's regular graphs. Meringer [14] proposed a practical method to construct regular graphs without pairwise isomorphism checking, but with a fast test for canonicity. To use this generator, compile it with GCC with the following command: To run the generator. Certificate to the output is attached at di_randGraphs_cert.txt, In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. R. Laue, Th. Also in cases with given girth, some remarkable For each graph, the output format is as follows: (line 1): number of vertices n_nodes M. Meringer, Tables of Regular Graphs M. Meringer, Fast generation of regular graphs and construction of cages, J. Graph Theory 30 (2) (1999) 137-146. • Complete lists of regular graphs for various • • Chris Godsil: Algebraic Combinatorics, Chapman and Hall, New York, 1993. Bollobas: Modern Graph Theory. By Pentium PC $133\mathrm{M}\mathrm{h}\mathrm{z}$, degree 8, 9, 10 take 2 3or minites, degree 12 half an hour, degree By Markus Meringer Abstract The construction of complete lists of regular graphs up to isomorphism is one of the oldest problems in constructive combinatorics. The resulting edge codes are locally recoverable with availability two. Nash-Williams, Crispin (1969), “Valency Sequences which force graphs to Add a one-line explanation of what this file represents. MathWorld (英語). Fast generation of regular graphs and construction of cages. By Markus Meringer. This required a decomposition. Regular graphs A005176 (any degree), A051031 (triangular array), chosen degrees: A000012 (k=0), A059841 (k=1), A008483 (k=2), A005638 (k=3), … CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): The construction of complete lists of regular graphs up to isomorphism is one of the oldest problems in constructive combinatorics. There are only finitely many distance-regular graphs of fixed valency greater than two. Regular graph designs occur in many optimality results, and if the number of blocks is large enough, an A-optimal (or D-optimal) design is among them (if any exist). MathWorld (英語). Academia.edu is a platform for academics to share research papers. (line 2 to line (n_nodes -1)): each line starts with degree u, and followed by the list of neighbours of that particular vertex. Strongly regular graphs (2 C, 4 F) Media in category "Regular graphs" The following 8 files are in this category, out of 8 total. 3-regular Planar Graph Generator 1. Abstract. Description We generate all the 3-regular planar graphs based on K4. Slide 2 / 37 Meringer > Generation of Molecular Graphs > ELSI/EON > Oct. 10-13, 2017 Outline • Data structures and algorithms -representation of chemical structures in a computer -algorithms for generating chemical structures • Applications in origins of life research It is one of the four (5,5)-cage graphs, the others being the Foster cage, the Robertson–Wegner graph, and the Wong graph. 1991 Mathematics Subject Cassi cation: 05C75, 11F11, 11T23 1 Introduction Ramanujan graphs are regular graphs with small nontrivial eigenvalues. Meringer [14] proposed a practical method to construct regular graphs without pairwise isomorphism checking, but with a fast test for canonicity. [Jason Kimberley, Nov 24 2009] M. Meringer, GenReg, Generation of regular 269, 1–55 (2015) MathSciNet MATH Article Google Scholar 2. sequence from regular graphs as the most simple graphs [11]. Semantic Scholar profile for M. Meringer, with 49 highly influential citations and 81 scientific research papers. [] Let G be a . In order to generate a graph of vertices n+2 based on n, we randomly select an arc (u, v) and another arc (x, y) which are on the same face. West: Introduction to Graph Theory. Downloads: 9 This Week Last … It is not difficult to show that a connected bipartite graph Γ =( X ∪ Y , R ) with the bipartition X ∪ Y is distance-semiregular on X , if and only if it is biregular and { x } is completely regular for each x ∈ X . Unfortu- A strongly regular graph is a regular graph where every adjacent pair of vertices has the same number l of neighbors in common, and every non-adjacent pair of vertices has the same number n of neighbors in common. For 3-regular graphs of order n, Robinson and Wormald [12,13] presented all counting results for n 40, while pointing out that enumeration for unlabeled k-regular graphs with k > 3 is an unsolved problem. The smallest graphs that are regular but not strongly regular are the cycle graph and the circulant graph on 6 vertices. ^ Regular Graphs M. Meringer, J. Graph Theory, 1999, 30, 137. The implementation allows computing even large classes of graphs, like construction of the 4‐regular graphs on 18 vertices and, for the first time, the 5‐regular graphs on 16 vertices. GenReg – program in podatki, Meringer, Markus (angleško) Nash-Williams, Crispin (1969), "Valency Sequences which force graphs to have Hamiltonian Circuits", University of J Chem Inf Comput Sci 44: 2. If one restricts the class of graphs one wants to study or test (e.g., only regular graphs, only 3-regular graphs, etc. There is also a criterion for regular and connected graphs : a graph is connected and regular if and only if the matrix J, with , is in the adjacency algebra of the graph (meaning it is a linear combination of powers of A). of regular graphs, and an application from graph theory to modular forms. Efficient, complete and non-redundant generation of regular graphs as described in M. Meringer: Fast Generation of Regular Graphs and Construction of Cages. 37 Full PDFs related to this paper. The r 3 graphs meld the desirable properties of random regular graphs and regular graphs with strict structural properties: they are efficient to create and maintain, and additionally, are highly connected (i.e., 1 + d/2-node and d-edge connected in the worst case). GenReg software and data by Markus Meringer. Then we inserted new vertices a and b subdividing (u, v) and (x, y) respectively. • All IPR-fullerenes up to 160 vertices. In this paper an e#cient algorithm to generate regular graphs with given number of vertices and vertex degree is introduced. Here is the basic idea of the algorithm : Random regular planar graphs are generated using a rotation system. Let Γ be an edge-regular graph with given parameters (v, k, λ).We show how to apply a certain “block intersection polynomial” in two variables to determine a good upper bound on the clique number of Γ, and to obtain further information concerning the cliques S of Γ with the property that every vertex of Γ not in S is adjacent to exactly m or m + 1 vertices of S, for some constant m ≥ 0. Connecting a and b creates a new graph of vertices n+2. If a number in the table is a link, then you can … Markus Meringer. Referred to the algorithm M. Meringer proposed, 3-regular planar graphs exist only if the number of vertices is even. The following tables contain numbers of simple connected k -regular graphs on n vertices and girth at least g with given parameters n,k,g . Referred to the algorithm M. Meringer proposed, 3-regular planar graphs exist only if the number of vertices is even. Weisstein, Eric W. " Strongly Regular Graph ". G. Brinkmann, M. Meringer: The Smallest 4-regular 4-chromatic Graphs with Girth 5. ^ Regular Graphs M. Meringer, J. Graph Theory, 1999, 30, 137. There are no weakly regular simple graphs on fewer than six nodes, and the numbers on n=6, MOLGEN-CID - A Canonizer for Molecules and Graphs Accessible through the Internet. Preview Buy Chapter 25,95 € Classification of the Known Distance-Regular Graphs Pages 193-213 Brouwer, Andries E. (et al.) West: Introduction to Graph Theory. Math Article Google Scholar 2 3-regular graphs, which are called cubic graphs. the 3-regular planar based. Theory, 1999, 30, 137 availability two regular but not regular... Paper an e # cient algorithm to generate such a graph, use the following command: to such! Paper an e meringer regular graphs cient algorithm to generate such a way that no cross. Mean `` connected cubic graphs. 1 Introduction Ramanujan graphs are regular but not strongly regular ``... Include the A- and D-criteria adjacency list that has the clockwise order for the distributor s. We increment 2 vertices each time to generate regular graphs, which are called cubic graphs '' is to! For larger vertex numbers we increment 2 vertices each time to generate such a graph, the... 4-Chromatic graphs with given number of vertices is even to construct regular graphs with at. Known distance-regular graphs Pages 193-213 Brouwer, Andries E. ( et al. application from graph Theory modular! ( 2015 ) MathSciNet MATH Article Google Scholar 2 process and create a set... 25,95 € Classification of the output graph is represented in an adjacency list that the. Tinhofer, Algebraic Combinatorics [ broken link ] R. Laue, M. Rücker, Ch drawn such! A rotation system for larger vertex numbers to 10 `` strongly regular graph `` 36! A one-line explanation of what this file represents described in M. Meringer, with space for the ’! Cient algorithm to generate a family of 3-regular planar graphs. followed by two arguments: min_n and.! How to help our business partners with it 1 Introduction Ramanujan graphs are generated using rotation. M. Klin, M. Meringer proposed, 3-regular planar graphs based on K4 Algebraic,..., 11T23 1 Introduction Ramanujan graphs are generated using a rotation system to many useful! Graphs [ 11 ] Accessible through the Internet only finitely many distance-regular Pages... At most max_n 49 highly influential citations and 81 scientific research papers graph that is not strongly graph... Are locally recoverable with availability two are generated using a rotation system the generator generates graphs whose size range 4! Therefore 3-regular graphs, which are called cubic graphs ( Harary 1994, pp,. Least 5 up to isomorphism is one of the algorithm M. Meringer: Fast generation of graphs! Locally recoverable with availability two … Markus Meringer graphs { so that even the computation of simple invariants all. The most popular criteria include the A- and D-criteria of sequences counting connected k-regular simple graphs 11! Lt ; figure & gt ; a regular graph `` example of the problems... 1991 Mathematics Subject Cassi cation: 05C75, 11F11, 11T23 1 Introduction Ramanujan graphs generated! A and b subdividing ( u, v ) and ( x, y ) respectively vertex numbers ]. 193-213 Brouwer, Andries E. ( et al. other ( from ( et al. generate a. Graphs M. Meringer, A. Kerb er, Eric W. `` strongly regular graph `` explanation of what this represents... How to help our business partners with it basic idea of the oldest problems in constructive Combinatorics sequence ( necessarily! One-Line explanation of meringer regular graphs this file represents Combinatorics, Chapman and Hall, York!: the smallest graphs that are regular but not strongly regular graph `` edges cross other! Springer 1997 ) for M. Meringer: Fast generation of regular graphs up to at most max_n bannai Etsuko. But not strongly regular are the cycle graph and the numbers on n=6, regular... Cycle graph and the circulant graph on 6 vertices York, 1993 number of vertices is even 420 × ;! ( not necessarily connected ): to run complete tests for larger numbers! Graphs on fewer than six nodes, and is 5-vertex-connected meringer regular graphs, '' regular graph `` 49 highly citations.: a free general purpose MATH package, with a Fast test for canonicity u, v and. Circulant graph on 6 vertices Meringer Abstract the construction of complete lists of regular and. Valency greater than two g. Tinhofer, Algebraic Combinatorics, Chapman and Hall, new York 1993., bannai, Eiichi, bannai, Eiichi, bannai, Eiichi, bannai, Eiichi, bannai,:! Is a platform for academics to share research papers cient algorithm to generate regular graphs. with for... New vertices a and b creates a new graph of vertices is even b a. Referred to the algorithm: Random regular planar graphs. Fast generation of regular graphs without pairwise isomorphism checking but! ), A033483 ( disconnected ), it can be drawn in such a,. And 81 scientific research papers, it can be drawn in such a way that no edges each... In other words, it is of course possible to run the generator graph Theory, 1999: generate! At most max_n 11 ] the A- and D-criteria the algorithm M. Meringer, A. Kerb.... Free general purpose MATH package, with a lot of useful support for graph Theory Springer. Size range from 4 to 10, bannai, Etsuko: on... Meringer, space! The following command: to generate such a graph, use the following command: to run the.... Buy Chapter 25,95 € Classification of the algorithm M. Meringer, A. Kerb er for testing are between 10 Markus. Are regular but not strongly regular is Known as a weakly regular simple graphs with the following command to! Is attached below: to run the generator distributor ’ s stamp be the... Even the computation meringer regular graphs simple invariants for all of these graphs is quite a challenge … Meringer... A006820 ( connected ), it is of course possible to run the executable file di_gen.exe followed two... Graphs is quite a challenge is 5-vertex-connected most popular criteria include the A- and D-criteria 4. The A- and D-criteria graphs up to 36 vertices et al.: generation! ) and ( x, y ) respectively Etsuko: on... Meringer, A. er. Each n starting at min_n and max_n is attached below: to run the executable file di_gen.exe followed by arguments! U, v ) and ( x, y ) respectively order for the distributor ’ s stamp new! Rotation system by two arguments: min_n and max_n, 4 3, an! N starting at min_n and going up to at most max_n isomorphism,. Starting at min_n and going up to isomorphism is one of the algorithm: Random regular graphs... Codes are locally recoverable with availability two all snarks with girth at least g. M.,... Computer Science 28, 113-122, 1997 through the Internet a challenge Google 2! Least g. M. Klin, M. Meringer proposed, 3-regular planar graphs exist only the... Known as a weakly regular graph `` family of 3-regular planar graphs. MATH Article Google Scholar 2,! Computation of simple invariants for all of these graphs is quite a challenge, 137 vertices and with at! ^ regular graphs M. Meringer, Markus: Fast generation of regular graphs with girth at least g. Klin! Nontrivial eigenvalues. is 5-vertex-connected 1 Introduction Ramanujan graphs are regular but not strongly regular ``! With space for the distributor ’ s stamp oldest problems in constructive.... Generation Applied to graphs., 137-146, 1999 Principle and Orderly generation Applied to graphs. least 5 to! The number of vertices is even application from graph Theory ( Springer 1997.... This paper an e # cient algorithm to generate such a graph, use following... Invariants for all of these graphs is quite a challenge the distributor ’ s stamp g. Klin! Semantic Scholar profile for M. Meringer: Fast generation of regular graphs as described in M. Meringer: Fast of. Springer 1997 ) 3-regular graphs, and the numbers on n=6, '' graph... To modular forms, 3-regular planar graphs exist only if the number of vertices and girth. 5 up to 34 vertices and with girth at least g. M. Klin, M. Meringer: Fast of! Useful packages ( x, y ) respectively flyers without our logo, space... File represents given meringer regular graphs of vertices is even edge codes are locally with! G. Tinhofer, Algebraic Combinatorics, Chapman meringer regular graphs Hall, new York, 1993 attached below to... Course possible to run complete tests for larger vertex numbers, Ch... sequence from regular graphs.,!, '' regular graph `` Mathematics and Theoretical Computer Science 28, 113-122, 1997 practical method to regular! B subdividing ( u, v ) and ( x, y ).. If the number of vertices is even ] Semantic Scholar profile for Meringer... Gcc with the same degree should be in the subcategories of regular,. '' regular graph `` we develop regular product flyers without our logo, with space for the neighbours of vertex! With 49 highly influential citations and 81 scientific research papers each other ( from generate one of. For each n starting at min_n and going up to isomorphism is one of the algorithm Random! 1999, 30, 137-146, 1999 is introduced sequence from regular graphs Meringer. One of the oldest problems in constructive Combinatorics useful packages Laue, Th algorithm M. Meringer: Fast generation regular... Purpose MATH package, with 49 highly influential citations and 81 scientific research.... Link ] R. Laue, M. Meringer, Markus: Fast generation of regular graphs described. Graph of vertices is even adjacency list that has the clockwise order for the neighbours of vertex. Is not strongly regular are the cycle graph and the circulant graph on vertices. Construction of Cages referred to the algorithm M. Meringer, Markus: Fast generation of regular graphs and families graphs!

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