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A graph G is said to be locally X, where X is a graph (or class of graphs), when for every vertex v, the graph induced on G by the set of adjacent vertices of V (sometimes ...

A graph G is distance transitive if its automorphism group is transitive on pairs of vertices at each pairwise distance in the graph. Distance-transitivity is a ...

The m×n rook complement graph K_m square K_n^_ is the graph complement of the m×n rook graph. It has vertex count mn and edge count 2(m; 2)(n; 2), where (n; k) is a binomial ...

A strongly regular graph with parameters (n,k,a,c) has graph eigenvalues k, theta, and tau, where theta = ((a-c)+sqrt(Delta))/2 (1) tau = ((a-c)-sqrt(Delta))/2 (2) where ...

A connected graph G is distance-regular if for any vertices x and y of G and any integers i,j=0, 1, ...d (where d is the graph diameter), the number of vertices at distance i ...

A sextic graph is a regular graph of degree six. The numbers of simple sextic graphs on n=7, 8, ... nodes are 1, 1, 4, 21, 266, 7846, 367860, ... (OEIS A006822). Examples are ...

The Brouwer-Haemers graph is the unique strongly regular graph on 81 vertices with parameters nu=81, k=20, lambda=1, mu=6 (Brouwer and Haemers 1992, Brouwer). It is also ...

A k-regular simple graph G on nu nodes is strongly k-regular if there exist positive integers k, lambda, and mu such that every vertex has k neighbors (i.e., the graph is a ...

The Schläfli graph is a strongly regular graph on 27 nodes which is the graph complement of the generalized quadrangle GQ(2,4). It is the unique strongly regular graph with ...

The Goddard-Henning graph, illustrated above in several embeddings, is the 9-node planar graph of graph diameter 2 having domination number gamma=3. It was first constructed ...