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Let G be a k-regular graph with girth 5 and graph diameter 2. (Such a graph is a Moore graph). Then, k=2, 3, 7, or 57. A proof of this theorem is difficult (Hoffman and ...

A black bishop graph is a graph formed from possible moves of a bishop chess piece, which may make diagonal moves of any length on a chessboard (or any other board), when ...

A lattice graph, also known as a mesh graph or grid graph, is a graph possessing an embedding in a Euclidean space R^n that forms a regular tiling. Examples include grid ...

The 12-vertex graph consisting of a cube in which two opposite faces (say, top and bottom) have edges drawn across them which connect the centers of opposite sides of the ...

The Leonard graph is a distance-regular graph on 288 vertices (Brouwer et al. 1989, p. 369) with intersection array {12,11,10,7;1,2,5,12}. It is however not ...

A simple unlabeled graph on n vertices is called pancyclic if it contains cycles of all lengths, 3, 4, ..., n. Since a pancyclic graph must contain a cycle of length n, ...

A graph is said to be regular of degree r if all local degrees are the same number r. A 0-regular graph is an empty graph, a 1-regular graph consists of disconnected edges, ...

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 (Delta,D)-graph is a graph with maximum vertex degree Delta and diameter at most D. The order of a graph with degree Delta of diameter D is bounded by ...

A graph with projective plane crossing number equal to 0 may be said to be projective planar. Examples of projective planar graphs with graph crossing number >=2 include the ...