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The Paley graph of order q with q a prime power is a graph on q nodes with two nodes adjacent if their difference is a square in the finite field GF(q). This graph is ...

A noneulerian graph is a graph that is not Eulerian. The numbers of simple noneulerian graphs on n=1, 2, ... nodes are 2, 3, 10, 30, 148, 1007, 12162, 272886, ... (OEIS ...

The great rhombicuboctahedral graph is the cubic Archimedean graph on 48 nodes and 72 edges that is the skeleton of the great rhombicuboctahedron as well as the great ...

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 middle layer graph of order n is the graph whose vertex set consists of all bitstrings of length 2n+1 that have exactly n or n+1 entries equal to 1, with an edge between ...

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 ...

The great snub dodecicosidodecahedral graph is the skeleton of the great snub dodecicosidodecahedron, illustrated above in a few embeddings. It will be implemented in a ...

The theorem, originally conjectured by Berge (1960, 1961), that a graph is perfect iff neither the graph nor its graph complement contains an odd graph cycle of length at ...

An automorphic graph is a distance-transitive graph Gamma for which the automorphism group Aut(Gamma) acts primitively on the vertices of Gamma and is not a complete graph or ...

The truncated great dodecahedral graph is the skeleton of the small stellated truncated dodecahedron and truncated great dodecahedron. It is illustrated above in a number of ...