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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 graph distance matrix, sometimes also called the all-pairs shortest path matrix, is the square matrix (d_(ij)) consisting of all graph distances from vertex v_i to vertex ...

The cube of a graph is defined as its third graph power.

A Berge graph is a simple graph that contains no odd graph hole and no odd graph antihole. The strong perfect graph theorem asserts that a graph is perfect iff it is a Berge ...

The Reye graph is the transposition graph G_4 of order 4.

A reflexive graph is a pseudograph such that each vertex has an associated graph loop.

The Pasch graph is the Levi graph of the Pasch configuration. The Pasch graph is edge-transitive but not vertex-transitive, but fails to be semisymmetric since it is not ...

A graph G whose line graph is L(G) is called the root graph R(L(G)) of L(G). In order words, R(L(G))=G. The root graph of a connected graph is unique except for K_3=C_3 (the ...

Cubic graphs, also called trivalent graphs, are graphs all of whose nodes have degree 3 (i.e., 3-regular graphs). Cubic graphs on n nodes exists only for even n (Harary 1994, ...

A 1-factor of a graph G with n graph vertices is a set of n/2 separate graph edges which collectively contain all n of the graph vertices of G among their endpoints.