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A nonplanar graph G is said to be critical nonplanar if the removal of a vertex results in a planar graph for every vertex of G. Critical nonplanar graphs differ from apex ...

The n-cycle complement graph C^__n is the graph complement of the cycle graph C_n. Cycle complement graphs are special cases of circulant graphs. The first few are ...

A uniquely Hamiltonian graph is a graph possessing a single Hamiltonian cycle. Classes of uniquely Hamiltonian graphs include the cycle graphs C_n, Hanoi graphs H_n, ladder ...

A graph is said to be unswitchable if it cannot be reduced to another graph with the same degree sequence by edge-switching. Conversely, a graph that can be reduced to ...

A string figure is any pattern produced when a looped string is spanned between two hands and is twisted and woven in various manners around the fingers and the wrists. The ...

The cocktail party graph of order n, also called the hyperoctahedral graph (Biggs 1993, p. 17), n-octahedron graph O_n (Jungerman and Ringel 1978), matching graph (Arvind et ...

A uniquely k-colorable graph G is a chi-colorable graph such that every chi-coloring gives the same partition of G (Chao 2001). Examples of uniquely minimal colorable classes ...

The Petersen graph is the cubic graph on 10 vertices and 15 edges which is the unique (3,5)-cage graph (Harary 1994, p. 175), as well as the unique (3,5)-Moore graph. It can ...

The clique polynomial C_G(x) for the graph G is defined as the polynomial C_G(x)=1+sum_(k=1)^(omega(G))c_kx^k, (1) where omega(G) is the clique number of G, the coefficient ...

One would think that by analogy with the matching-generating polynomial, independence polynomial, etc., a cycle polynomial whose coefficients are the numbers of cycles of ...