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The Heawood four-color graph is the 25-node planar graph illustrated above that tangles the Kempe chains in Kempe's algorithm and thus provides an example of how Kempe's ...

An Ore graph is a graph that satisfies Ore's theorem, i.e., a graph G for which the sums of the degrees of nonadjacent vertices is greater than or equal to the number of ...

The Poussin graph is the 15-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 small rhombicosidodecahedral graph is a quartic graph on 60 nodes and 120 edges that corresponds to the skeleton of the small rhombicosidodecahedron, as well as the great ...

The small rhombicuboctahedral graph is a quartic graph on 24 nodes and 48 edges that corresponds to the skeleton of the small rhombicuboctahedron. It has graph diameter 5, ...

The ABC (atom-bond connectivity) energy of a graph is defined as the graph energy of its ABC matrix, i.e., the sum of the absolute values of the eigenvalues of its ABC matrix.

The chromatic number of a graph is at most the maximum vertex degree Delta, unless the graph is complete or an odd cycle, in which case Delta+1 colors are required.

Let D be a set of positive numbers containing 1, then the D-distance graph X(D) on a nonempty subset X of Euclidean space is the graph with vertex set X and edge set ...

The Dürer graph is the skeleton of Dürer's solid, which is the generalized Petersen graph GP(6,2). It is illustrated above in a number of embeddings. It is implemented in the ...

The edge multiplicity of a given end vertex in a multigraph is the number of multiple edges sharing that end vertex. The maximum edge multiplicity in such a graph is known as ...