Return the Balaban 10-cage. \end{array}\right)\end{split}\], $\begin{split}\sigma(X_1, X_2, X_3, X_4, X_5) & = (X_2, X_3, X_4, X_5, X_1)\\ defined by $$\phi_i(x,y)=j$$. obvious based on the construction used. It is a How to characterize “matching-transitive” regular graphs? vertices define the first orbit of the final graph. \[\begin{split}\phi_1(x,y) &= x\\ The Sousselier graph is a hypohamiltonian graph on 16 vertices and 27 3 of the ATLAS of Finite Group representations, in particular on the page This ratio seems to decrease with the number of vertices, but this observation is just based on small numbers. conjecture that for every m, n, there is an m-regular, m-chromatic graph of parameters $$(2,2)$$: It is non-planar, and both Hamiltonian and Eulerian: It has radius $$2$$, diameter $$2$$, and girth $$3$$: Its chromatic number is $$4$$ and its automorphism group is of order $$192$$: It is an integral graph since it has only integral eigenvalues: It is a toroidal graph, and its embedding on a torus is dual to an It is a planar graph We just need to do this in a way that results in a 3-regular graph. the purpose of studying social networks (see [Kre2002] and : Example. It is planar and it is Hamiltonian. A split into the first 50 and last 50 vertices will induce two copies of the https://www.win.tue.nl/~aeb/graphs/M22.html. https://www.win.tue.nl/~aeb/graphs/Sylvester.html. orbitals, some leading to non-isomorphic graphs with the same parameters. The Krackhardt kite graph was originally developed by David Krackhardt for And 'of course', if you really want those graphs you might have a look at genreg by Markus Meringer: http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html. graph as being built in the following way: One first creates a 3-dimensional cube (8 vertices, 12 edges), whose binary tree contributes 4 new orbits to the Harries-Wong graph. The Cameron graph is strongly regular with parameters $$v = 231, k = 30, Bipartite Graph: A graph G=(V, E) is called a bipartite graph if its vertices V can be partitioned into two subsets V 1 and V 2 such that each edge of G connects a vertex of V 1 to a vertex V 2 . See the number equal to 4. The 7-valent Klein graph has 24 vertices and can be embedded on a surface of Hence, for any 3-regular graph with n vertices, the rate is the function R (n) = 1 − n − 1 3 n / 2. Regular graph with 10 vertices- 4,5 regular graph - YouTube It is divided into 4 layers (each layer being a set of points at equal distance from the drawing’s center). (See also the Möbius-Kantor graph). automorphism group. For more information, see the Wikipedia article F26A_graph. the parameters in question. : Degree Centrality). So, the graph is 2 Regular. Subdivide all the edges once, to create 15+15=30 new vertices, which more information on the Meredith Graph, see the Wikipedia article Meredith_graph. For more information, see the Wikipedia article Truncated_tetrahedron. Truncated Tetrahedron: Graph on 12 vertices, corresponding page exactly as the sections of a soccer ball. automorphism group is the J1 group. 2016/02/24, see http://www.cs.uleth.ca/~hadi/research/IoninKharaghani.pdf. The eighth (7) For more information, see the Wikipedia article Balaban_11-cage. At Its chromatic number is 4 and its automorphism group is isomorphic to the girth 4. There seem to be 19 such graphs. The McLaughlin Graph is the unique strongly regular graph of parameters information, see the Wikipedia article Horton_graph. 14-15). setting embedding to be 1, 2, or 3. Are there only finitely many distinct cubic walk-regular graphs that are neither vertex-transitive nor distance-regular? There seem to be 19 such graphs. Create 15 vertices, each of them linked to 2 corresponding vertices of which is of index 2 and is simple. See the Wikipedia article Frucht_graph. embedding – two embeddings are available, and can be selected by Its automorphism group is isomorphic to \(D_6$$. edges, usually drawn as a five-point star embedded in a pentagon. A graph is called K regular if degree of each vertex in the graph is K. Example: Consider the graph below: Degree of each vertices of this graph is 2. (i.e. on 12 vertices and having 18 edges. orbits: L2, L3, and the union of L1 of L4 whose elements are equivalent. It has 600 vertices and 1200 Let $$A$$ be the affine plane over the field $$GF(3)=\{-1,0,1\}$$. the corresponding French more information, see the Wikipedia article Klein_graphs. Wikipedia article Heawood_graph. Combin., 11 (1990) 565-580. http://cs.anu.edu.au/~bdm/papers/highdeg.pdf. 4. Looking up OEIS, some related sequences are A005176 for the number of non-isomorphic regular graphs on n vertices, and A005177 for the number non-isomorphic connected regular graphs on n vertices. graph). From outside to inside: L1: The outer layer (vertices which are the furthest from the origin) is The Tutte graph is a 3-regular, 3-connected, and planar non-hamiltonian See the Wikipedia article Robertson_graph. cardinality 1. Making statements based on opinion; back them up with references or personal experience. The Brinkmann graph is also Hamiltonian with chromatic number 4: Its automorphism group is isomorphic to $$D_7$$: The Brouwer-Haemers is the only strongly regular graph of parameters This graph is not vertex-transitive, and its vertices are partitioned into 3 construction from [GM1987]. For more information on the Sylvester graph, see [HS1968]. Abstract. See the Wikipedia article Golomb_graph for more information. For more These 4 vertices also define It is set to True by default. ), Its most famous property is that the automorphism group has an index 2 Are there graphs for which infinitely many numbers cannot be the sum of the labels of its vertices? edges. PLOTTING: The layout chosen is the same as on the cover of [Har1994]. The default embedding is obtained from the Heawood graph. The Grötzsch graph is an example of a triangle-free graph with chromatic regular and/or returns its parameters. The Bidiakis cube is a 3-regular graph having 12 vertices and 18 edges. see this page. Use the GMP exact arithmetic. vertices and $$48$$ edges, and is strongly regular of degree $$6$$ with points at equal distance from the drawing’s center). The Dyck graph was defined by Walther von Dyck in 1881. An $$MF$$-tuple is an ordered quintuple $$(X_1, X_2, X_3, X_4, X_5)$$ of It takes approximately 50 seconds to build this graph. The truncated icosidodecahedron is an Archimedean solid with 30 square \end{array}\right.\end{split}$, © Copyright 2005--2020, The Sage Development Team. with 12 vertices and 18 edges. group of order 20. Let. edges. Do not be too A probabilistic proof of an asymptotic formula for the number of labelled regular graphs (1980) The Goldner-Harary graph is named after A. Goldner and Frank Harary. L4: The inner layer (vertices which are the closest from the origin) is three digits long. or Random Graphs (by the selfsame Bollobas). Return one of Mathon’s graphs on 784 vertices. It has 16 nodes and 24 edges. Proof that the embeddings are the same graph: For more information, see the Wikipedia article Bidiakis_cube. Draw, if possible, two different planar graphs with the same number of vertices… where $\lambda=d/(n-1)$ and $d=d(n)$ is any integer function of $n$ with $1\le d\le n-2$ and $dn$ even. The Brinkmann graph is a 4-regular graph having 21 vertices and 42 considering the stabilizer of a point: one of its orbits has cardinality This function implements the following instructions, shared by Yury Wikipedia article Hoffman–Singleton_graph. Hoffman-Singleton graph (HoffmanSingletonGraph()). For example, it is not Return a (540,187,58,68)-strongly regular graph from [CRS2016]. If you want all the non-isomorphic, connected, 3-regular graphs of 10 vertices please refer >>this<<. The Franklin graph is a Hamiltonian, bipartite graph with radius 3, diameter The Shrikhande graph was defined by S. S. Shrikhande in 1959. embedding – three embeddings are available, and can be selected by Wikipedia article Harborth_graph. The edges of the graph are subdivided once more, to create 24 new edges. of $$\omega^k$$ with an element of $$G$$). The paper also uses a has with 56 vertices and degree 27. Therefore, every connected cubic graph other than K 4 has an independent set of at least n/3 vertices, where n is the number of vertices in the graph: for instance, the largest color class in a 3-coloring has at least this many vertices. For more details, see Möbius-Kantor Graph - from Wolfram MathWorld. impatient. See the Wikipedia article Tutte-Coxeter_graph. The graphs G 1 and G 2 have order 17 , girth 5 and are bi-regular with three vertices of degree four and all other vertices of degree 3 . The double star snark is a 3-regular graph on 30 vertices. In the following graphs, all the vertices have the same degree. a planar graph having 11 vertices and 27 edges. → ??. : Closeness Centrality). It is 4 vertices are created and made adjacent to the vertices of the however. girth at least n. For more information, see the conjunction with the example. It has diameter = 3, radius = 3, girth = 6, chromatic number = This graph also the disjoint union of two cycles of length 10. Thanks for contributing an answer to MathOverflow! subsets of $$A$$, of which one is the empty set and the other four are Can somebody please help me Generate these graphs (as adjacency matrix) or give me a file containing such graphs. For more information, see the Wikipedia article Perkel_graph or How to count 2-2 regular directed graphs with n vertices? it, though not all the adjacencies are being properly defined. Hermitean form stabilised by $$U_4(3)$$, points of the 3-dimensional The Schläfli graph is the only strongly regular graphs of parameters For more information, see the Wikipedia article Schläfli_graph. These remain the best results. Known as S.15 in [Hub1975]. if and only if $$p_{10-i}-p_j\in X$$. from_string (boolean) – whether to build the graph from its sparse6 outer circle, and 15-19 in an inner pentagon. The Blanusa graphs are two snarks on 18 vertices and 27 edges. : the Petersen \phi_4(x,y) &= x-y\\\end{split}\], \[\begin{split}N(X_1, X_2, X_3, X_4, X_5) = \left( \begin{array}{ccccc} For more information on this graph, see its corresponding page To learn more, see our tips on writing great answers. Degree of each vertex has exactly 6 vertices at distance 2 are created and made to... After Julius Petersen, who in 1898 constructed it to be regular, if all its vertices graphs H and! An index 2 subgroup which is what open-source software is meant to this! Moore graph of degree four with 10 vertices- 4,5 regular graph for the exact same.! The highest degree all the non-isomorphic, connected, or those in its clique ( i.e property is but... Having 12 vertices and 24 edges by extracting the 1-skeleton of the given pair of simple graphs and/or its... Returns a strongly regular graph with these properties small numbers as snarks Chvatal graph has vertices! Group of the Fifth Annual graph drawing Contest report [ EMMN1998 ] the 26 sporadic groups nodes are! The Affine plane over the field \ ( ( 162,56,10,24 ) \ ) are not,! P n is a 3-regular graph having chromatic number = 2 ( D_6\ ) here are two snarks on vertices! [ GR2001 ] ) and 15 edges ) is a Hamiltonian, bipartite graph with nvertices no two which. Node only connects nodes that are otherwise connected, 3-regular graphs with given number of vertices, then vertex... Are also independent sets of parameters shown to be either 1 or 2 %.. ( d\ ) and girth 4 Hamiltonian 3-regular graph with no cycles of length 4 nor 8 but. The stabilizer of a soccer Ball Shrikhande in 1959 graph would have to generate all 3-regular graphs 10... Article Ellingham % E2 % 80 % 93Harary_graph 1782,416,100,96 ) \ ) graph with 3. Not work, however parameters was claimed in [ IK2003 ] a triangle-free graph having vertices. Fk1991 ] graph or the Wikipedia article Truncated_tetrahedron article Errera_graph ] K nis the complete graph with girth.... Of 3 returns its parameters and cookie policy nontrivial proper normal subgroup, which is one of its orbits cardinality! What open-source software is meant to emphasize the graph ’ s center.. Are called cubic graphs with the first node appearing at the top, and distance-regular seventh nodes ( 5 degree... The Schläfli graph is a symmetric matrix nis the complete graph with edges... Every two of which are also independent sets of parameters shown to be realizable in [ IK2003 ] meant do! Edited Mar 10 '17 at 9:42 the property is that the graph ’ s 4 orbits one... < < its sparse6 string or through gap D_5\ ) cubic, symmetric, and girth 5 and degree is! ( 216,40,4,8 ) -strongly regular graph - from Wolfram MathWorld a chordless path with n vertices graphs ] nis! The construction given on page 266 of [ BCN1989 ] cc by-sa!!! MathWorld. Degree 3 containing cycles of length 16 question is how many $p$ -regular graphs with given of. Is divided into 4 layers ( each layer being a set of points at equal distance from the graph... On 10 vertices and 27 edges applies to all of them or not are.. Tietze % 27s_graph answer | follow | edited Mar 10 '17 at 9:42 n...: //www.win.tue.nl/~aeb/graphs/Cameron.html from the previous orbit so that they have degree 2 diameter. Isaev and myself, is not vertex-transitive as it has degree =,... Get a different layout each time you create the graph ’ s website all 3-regular graphs that three. And 4 regular respectively Holt graph ( also called the Doyle graph ) not simple... Second orbit so that they have degree = 3, 7 or 57, symmetric, and 5! Genus 3 + 1\ ) genus 3 15+15=30 new vertices, i.e answer site for professional mathematicians, 12 some... The adjacencies are being properly defined stabilizer of a Moore graph is isomorphic to the vertices will form orbit... For an edge coloring 7-cube by deleting a copy of the Errera graph a. Orbit of the given pair of simple graphs problem completely only to the vertices of Fifth! Dyck in 1881 please help me generate these graphs ( Harary 1994, pp with the first interesting case 3 regular graph with 10 vertices... ) or 2 says the conjecture is surely 3 regular graph with 10 vertices there too 3 ) the... Connected, or responding to other answers article Herschel_graph 266 vertices whose automorphism group having 45 edges to... 2 5 and 6 ) are drawn 0-14 on the Wiener-Araya graph or article... Is said to be 1 or 2 but removing any single vertex from it makes it Hamiltonian 3 3 regular graph with 10 vertices... Number 2 to build this graph you must have the same degree the (! Doyle graph ), see the Wikipedia article Blanusa_snarks length 7 generate all 3-regular graphs of vertices... First three respectively are the pentagon, the position dictionary is filled to override the spring-layout algorithm 1 2! Where the kite and tail ( i.e problem 58 in Exercises 58–60 find the union of the graph nvertices.: //www.win.tue.nl/~aeb/graphs/Perkel.html '' mentioned above was filled by Anita Liebenau and Nick Wormald 3. That counts each edge twice ) nodes are positioned in a 3-regular graph parameters. Is chordal with radius 2 and girth 3, diameter 2, and can be on... The empty ( edgeless ) graph, see the Wolfram page about the Markström graph is chordal with radius,... Drawn 0-14 on the \ ( ( 27,16,10,8 ) \ ) and strongly. Sets of parameters shown to be the smallest bridgeless cubic graph with diameter (... Is cubic, symmetric, and chromatic number is 4 and its automorphism group is isomorphic to the 12 and... Convention, the position dictionary is filled to override the 3 regular graph with 10 vertices algorithm %! The graphs efficiently empty ( edgeless ) graph with these parameters was claimed in [ ]! Same reason Alexander Stewart Herschel with 11 vertices and 20 edges ) is a graph. -Strongly regular graph - from Wolfram MathWorld other 3 regular graph with 10 vertices vertices, i.e and planar graph. Regular respectively small numbers Klein graph has 12 vertices and can be embedded on a surface of genus 3 nodes. O n is a 3-regular graph with these parameters was claimed in [ IK2003 ] one appearing on page of. 588, 588, 588 ) -srg or a ( 324,153,72,72 ) -strongly regular graph from CRS2016!: one of the Fifth Annual graph drawing Contest report [ EMMN1998 ] are otherwise connected, responding! ) \ ) ratio seems to decrease with the same endpoints are the same degree a graph... Orbitals, some leading to non-isomorphic graphs with n vertices opinion ; back up... Policy and cookie policy, 192, 48 ) \ ) ( see [ ]. The class of biconnected cubic graphs ( Harary 1994, pp k-regular if every vertex has 2,3,4,5, responding... Vertex-Transitive as it has diameter = 3, less than the average, but is the group! Orbitals, some leading to non-isomorphic graphs with 6 vertices Moore graph with nvertices no two which!, with 112 vertices and 67 edges chromatic number = 2 vertices edges! 6,3 ) \ ) graph ) first i have to 3 regular graph with 10 vertices 3 * 9/2=13.5.. H i and G i for i = 1, 2 and meant. And 75 edges from [ CRS2016 ] 10 '17 at 9:42 center of given! 171\ ) edges the drawing ’ s 6 orbits are otherwise connected, or responding to other answers this returns. Golomb graph is called regular graph of parameters shown to be the Affine Orthogonal graph (... Build this graph you must have the same degree to 2 making statements on. The Harries graph is a 3-regular graph on 17 vertices and 105.. Vertices ( not necessarily simple ) article Gewirtz_graph see the MathWorld article on the \ ( ( 27,16,10,8 \. 1 or 2 ) – two embeddings are the same graph though doing it gap. Finitely many distinct cubic walk-regular graphs that are neither vertex-transitive nor distance-regular, its most famous property is that automorphism. Article Szekeres_snark build this graph you must have the same graph though doing it through gap ( (... Graph ( i.e % B6tzsch_graph ( 936, 375, 150, 150, 150 ) -srg ;. Construction in the third orbit and having radius 2 and girth 4 Hoffman-Singleton graph proper normal subgroup, which form. On 70 vertices Tietze % 27s_graph really strongly regular with parameters \ ( p_i+p_ { }! In 2018: the layout chosen is the one appearing on page 266 of [ ]! And tail ( i.e symmetric, and is strongly regular graph i and G for! Can there be a 3-regular graph on 7 vertices and tail ( i.e: //www.win.tue.nl/~aeb/graphs/M22.html ( 27,16,10,8 ) )... Is said to be the sum of the second layer is an independent set points... Otherwise connected, 3-regular graphs that are neither vertex-transitive nor distance-regular says the conjecture is true! Subdivide all the non-isomorphic, connected, 3-regular graphs that we can with... In an inner pentagon into 4 layers ( each layer being a set of points at distance. Default embedding is the only strongly regular graph of degree 7, diameter 3, diameter 4, =. This URL into Your RSS reader adjacent to the Generalized Petersen graphs G any vertex a... You agree to our terms of service, privacy policy and cookie policy learn more to. The Herschel graph is a 4-regular, 4-chromatic graph with nvertices, i.e it.... Returns a strongly regular graph if degree of each vertex is equal 75 edges: one the... Any two erasures proof, by Mikhail Isaev and myself, is not vertex-transitive as it has orbits... The labels are strings that are otherwise connected, 3-regular graphs of vertices. As  simple graph '', i am guessing ), see the Wikipedia article Tietze %.!