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The snub cubical graph is the Archimedean graph on 24 nodes and 60 edges obtained by taking the skeleton of the snub cube. It is a quintic graph, is planar, Hamiltonian, and ...

The great rhombicosidodecahedral graph is the Archimedean graph on 120 vertices and 180 edges that is the skeleton of the great rhombicosidodecahedron as well as the uniform ...

Vizing's theorem states that a graph can be edge-colored in either Delta or Delta+1 colors, where Delta is the maximum vertex degree of the graph. A graph with edge chromatic ...

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 ...

Bouwer graphs, a term coined here for the first time, are a family of regular graphs which includes members that are symmetric but not arc-transitive. Such graphs are termed ...

A unit-distance graph is a distance graph having an embedding in the Euclidean plane (unit-distance embedding) in which vertices are distinct points and all edges are of ...

A polyhedral nonhamiltonian graph is a graph that is simultaneously polyhedral and nonhamiltonian. The smallest possible number of vertices a nonhamiltonian polyhedral graph ...

A (v,g)-cage graph is a v-regular graph of girth g having the minimum possible number of nodes. When v is not explicitly stated, the term "g-cage" generally refers to a ...

The co-rank of a graph G is defined as s(G)=m-n+c, where m is the number of edges of G, n is the number of vertices, and c is the number of connected components (Biggs 1993, ...

The rank of a graph G is defined as r(G)=n-c, where n is the number of vertices on G and c is the number of connected components (Biggs 1993, p. 25).