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The graph neighborhood of a vertex v in a graph is the set of all the vertices adjacent to v including v itself. More generally, the ith neighborhood of v is the set of all ...

The Gosset graph is a 27-regular graph on 56 vertices which is the skeleton of the Gosset polytope 3_(21). It is a distance-regular graph with intersection array ...

The Hamming graph H(d,q), sometimes also denoted q^d, is the graph Cartesian product of d copies of the complete graph K_q. H(d,q) therefore has q^d vertices. H(d,q) has ...

The stacked book graph of order (m,n) is defined as the graph Cartesian product S_(m+1) square P_n, where S_m is a star graph and P_n is the path graph on n nodes. It is ...

The truncated dodecadodecahedral graph is the skeleton of the truncated dodecadodecahedron, which is the only uniform polyhedron for which this is the case. It will be ...

The Johnson graph J(n,k) has vertices given by the k-subsets of {1,...,n}, with two vertices connected iff their intersection has size k-1. Special classes are summarized in ...

A graph for which the relations between pairs of vertices are symmetric, so that each edge has no directional character (as opposed to a directed graph). Unless otherwise ...

The gear graph, also sometimes known as a bipartite wheel graph (Brandstädt et al. 1987), is a wheel graph with a graph vertex added between each pair of adjacent graph ...

A section of a graph obtained by finding its intersection with a plane.

For a connected graph G of graph diameter d, the distance-k graph G_k for k=1, ..., d is a graph with the same vertex set and having edge set consisting of the pairs of ...