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A cycle of a graph G, also called a circuit if the first vertex is not specified, is a subset of the edge set of G that forms a path such that the first node of the path ...

A simple unlabeled graph on n vertices is called pancyclic if it contains cycles of all lengths, 3, 4, ..., n. Since a pancyclic graph must contain a cycle of length n, ...

An automorphism of a graph is a graph isomorphism with itself, i.e., a mapping from the vertices of the given graph G back to vertices of G such that the resulting graph is ...

A graph cycle.

A simple graph, also called a strict graph (Tutte 1998, p. 2), is an unweighted, undirected graph containing no graph loops or multiple edges (Gibbons 1985, p. 2; West 2000, ...

A quartic vertex-transitive graph is a quartic graph that is vertex transitive. Read and Wilson (1988, pp. 164-166) enumerate all connected quartic vertex-transitive graphs ...

The triangle graph is the cycle graph C_3, which is isomorphic to the complete graph K_3 as well as to the complete tripartite graph K_(3×1)=K_(1,1,1) and the triangular ...

Let G be a group, and let S subset= G be a set of group elements such that the identity element I not in S. The Cayley graph associated with (G,S) is then defined as the ...

A nut graph is a graph on n>=2 vertices with adjacency matrix A such that A has matrix rank 1 and contains no 0 element (Sciriha 1998, 2008; Sciriha and Gutman, 1998; and ...

An antimagic graph is a graph with e graph edges labeled with distinct elements {1,2,...,e} so that the sum of the graph edge labels at each graph vertex differ.