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The n-dimensional Keller graph, sometimes denoted G_n (e.g., Debroni et al. 2011), can be defined on a vertex set of 4^n elements (m_1,...,m_n) where each m_i is 0, 1, 2, or ...

A planar hypohamiltonian graph is a hypohamiltonian graph that is also planar. A number of planar hypohamiltonian graphs are illustrated above. Chvátal (1973) first asked if ...

A bridge of a connected graph is a graph edge whose removal disconnects the graph (Chartrand 1985, p. 45; Skiena 1990, p. 177). More generally, a bridge is an edge of a ...

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 ...

There are several sorts of graphs referred to as "star graphs" in mathematics, computer science, and information processing. The most common sort of star is the n-star graph ...

In general, a graph product of two graphs G and H is a new graph whose vertex set is V(G)×V(H) and where, for any two vertices (g,h) and (g^',h^') in the product, the ...

The bandwidth of a connected graph G is the minimum matrix bandwidth among all possible adjacency matrices of graphs isomorphic to G. Equivalently, it is the minimum graph ...

Lovász (1970) conjectured that every connected vertex-transitive graph is traceable (Gould, p. 33). This conjecture was subsequently verified for several special orders and ...

Let S be a set and F={S_1,...,S_p} a nonempty family of distinct nonempty subsets of S whose union is union _(i=1)^pS_i=S. The intersection graph of F is denoted Omega(F) and ...

The order-n bouquet graph B_n is a pseudograph consisting of a single vertex with n self-loops. The bouquet graph B_1 is a pseudograph that can be considered to correspond to ...