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A graceful labeling (or graceful numbering) is a special graph labeling of a graph on m edges in which the nodes are labeled with a subset of distinct nonnegative integers ...

The (upper) vertex independence number of a graph, often called simply "the" independence number, is the cardinality of the largest independent vertex set, i.e., the size of ...

A line graph L(G) (also called an adjoint, conjugate, covering, derivative, derived, edge, edge-to-vertex dual, interchange, representative, or theta-obrazom graph) of a ...

LCF notation is a concise and convenient notation devised by Joshua Lederberg (winner of the 1958 Nobel Prize in Physiology and Medicine) for the representation of cubic ...

The pentagrammic antiprism is the uniform polyhedron with Maeder index 79 (Maeder 1997), Coxeter index 34 (Coxeter et al. 1954), and Har'El index 4 (Har'El 1993). It will be ...

A k-regular simple graph G on nu nodes is strongly k-regular if there exist positive integers k, lambda, and mu such that every vertex has k neighbors (i.e., the graph is a ...

The bipartite double graph, also called the Kronecker cover, Kronecker double cover, bipartite double cover, canonical double cover, or bipartite double, of a given graph G ...

A cubic vertex-transitive graph is a cubic graph that is vertex transitive. Read and Wilson (1998, pp. 161-163) enumerate all connected cubic vertex-transitive graphs on 34 ...

Let c_k be the number of vertex covers of a graph G of size k. Then the vertex cover polynomial Psi_G(x) is defined by Psi_G(x)=sum_(k=0)^(|G|)c_kx^k, (1) where |G| is the ...

An equilateral polyhedron is a polyhedron whose edges are all of equal length. Platonic solids, Archimedean solids, canonical antiprisms, and canonical prisms, Johnson ...