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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 ...

Graph smoothing, also known as smoothing away or smoothing out, is the process of replacing edges e^'=v_iv_j and e^('')=v_jv_k incident at a vertex v_j of vertex degree 2 by ...

The Harries-Wong graph is one of the three (3,10)-cage graphs, the other two being the (10,3)-cage known as the Balaban 10-cage and the Harries graph. The Harries-Wong graph ...

The truncated Witt graph is the graph on 506 vertices related to a 4-(23,8,4) design (Brouwer et al. 1989, p. 367). It is called the M_(23) graph by van Dam and Haemers ...

The Errera graph is the 17-node planar graph illustrated above that tangles the Kempe chains in Kempe's algorithm and thus provides an example of how Kempe's supposed proof ...

The genus gamma(G) of a graph G is the minimum number of handles that must be added to the plane to embed the graph without any crossings. A graph with genus 0 is embeddable ...

A path in a graph G is a subgraph of G that is a path graph (West 2000, p. 20). The length of a path is the number of edges it contains. In most contexts, a path must contain ...

A regular graph that is not strongly regular is known as a weakly regular graph. There are no weakly regular simple graphs on fewer than six nodes, and the numbers on n=6, 7, ...

There are several definitions of "almost Hamiltonian" in use. As defined by Punnim et al. (2007), an almost Hamiltonian graph is a graph on n nodes having Hamiltonian number ...

A rolling polyhedron graph is a graph obtained by rolling a polyhedral solid along a board whose tiles match up with the faces of the polyhedron being rolled. The vertices of ...