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An n-component of a graph G is a maximal n-connected subgraph.

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 Gray graph is a cubic semisymmetric graph on 54 vertices. It was discovered by Marion C. Gray in 1932, and was first published by Bouwer (1968). Malnič et al. (2002) ...

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 ...

A Mycielski graph M_k of order k is a triangle-free graph with chromatic number k having the smallest possible number of vertices. For example, triangle-free graphs with ...

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 Heawood graph is a cubic graph on 14 vertices and 21 edges which is the unique (3,6)-cage graph. It is also a Moore graph. It has graph diameter 3, graph radius 3, and ...

The longhorn graph is the graph on 7 vertices illustrated above. It is implemented in the Wolfram Language as GraphData["LonghornGraph"].

A connected graph is graph that is connected in the sense of a topological space, i.e., there is a path from any point to any other point in the graph. A graph that is not ...