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A (0,2)-graph is a connected graph such that any two vertices have 0 or 2 common neighbors. (0,2)-graphs are regular, and the numbers of (0,2)-graphs with vertex degree 0, 1, ...

Let S be a set of simple polygonal obstacles in the plane, then the nodes of the visibility graph of S are just the vertices of S, and there is an edge (called a visibility ...

A graph G on more than two vertices is said to be k-connected (or k-vertex connected, or k-point connected) if there does not exist a vertex cut of size k-1 whose removal ...

A graph corresponding to the skeleton of one of the Archimedean solids. There are 13 Archimedean graphs, all of which are regular, planar, polyhedral, and Hamiltonian. The ...

The odd graph O_n of order n is a graph having vertices given by the (n-1)-subsets of {1,...,2n-1} such that two vertices are connected by an edge iff the associated subsets ...

A connected graph G is said to be t-tough if, for every integer k>1, G cannot be split into k different connected components by the removal of fewer than tk vertices. The ...

The small rhombicosidodecahedral graph is a quartic graph on 60 nodes and 120 edges that corresponds to the skeleton of the small rhombicosidodecahedron, as well as the great ...

The utility problem posits three houses and three utility companies--say, gas, electric, and water--and asks if each utility can be connected to each house without having any ...

The Tilley graph is a polyhedral graph that arises in the investigation of Kempe chainsKempe Chain (Tilley 2018). It has 12 vertices, 29 edges, and 19 faces (one of which is ...

The skeleton of a trapezohedron may be termed a trapezohedral graph. n-trapezohedral graphs are illustrated above for n=3 to 10 in circular embeddings with the two interior ...