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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 ...

A bridged graph is a graph that contains one or more graph bridges. Examples of bridged graphs include path graphs, ladder rung graphs, the bull graph, star graphs, and ...

The word "rigid" has two different meaning when applied to a graph. Firstly, a rigid graph may refer to a graph having a graph automorphism group containing a single element. ...

The Doyle graph, sometimes also known as the Holt graph (Marušič et al. 2005), is the quartic symmetric graph on 27 nodes illustrated above in several embeddings. It is ...

The Livingstone graph is a distance-transitive graph on 266 vertices defined in terms of the Janko group J_1. It has intersection array {11,10,6,1;1,1,5,11}. The Livingstone ...

A complete multipartite graph is a graph that is a complete k-partite graph for some positive integer k (Chartrand and Zhang 2008, p. 41).

The kite graph is the 5-vertex graph illustrated above (Brandstädt et al. 1987, p. 18). It is implemented in the Wolfram Language as GraphData["KiteGraph"]. Unfortunately, ...

The n-path complement graph P^__n is the graph complement of the path graph P_n. The first few are illustrated above. Since P_4 is self-complementary, P^__4 is isomorphic to ...

The graph complement of a perfect graph is itself perfect. Originally known as the weak perfect graph conjecture (Fulkerson 1971), the result was subsequently proved by ...

A functional graph is a directed graph in which each vertex has outdegree one, and can therefore be specified by a function mapping {1,...,n} onto itself. Functional graphs ...