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Given a planar graph G, its geometric dual G^* is constructed by placing a vertex in each region of G (including the exterior region) and, if two regions have an edge x in ...

The Wiener-Araya graph (Wiener and Araya 2009) is the 42-vertex graph illustrated above that was the smallest known example of a planar hypohamiltonian graph, beating the ...

A notion introduced by R. M. Wilson in 1974. Given a finite graph G with n vertices, puz(G) is defined as the graph whose nodes are the labelings of G leaving one node ...

The 16-cell beta_4 is the finite regular four-dimensional cross polytope with Schläfli symbol {3,3,4}. It is also known as the hyperoctahedron (Buekenhout and Parker 1998) or ...

A graph G having chromatic number chi(G)<=k is called a k-colorable graph (Harary 1994, p. 127). In contrast, a graph having chi(G)=k is said to be a k-chromatic graph. Note ...

A graph with projective plane crossing number equal to 0 may be said to be projective planar. Examples of projective planar graphs with graph crossing number >=2 include the ...

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 ...

The honeycomb toroidal graph HTG(m,2n,s) on 2nm vertices for m, n, and s positive integers satisfying n>1 and m+s is even is defined as the graph on vertex set u_(ij) for ...

A graph is k-edge-connected if there does not exist a set of k-1 edges whose removal disconnects the graph (Skiena 1990, p. 177). The maximum edge connectivity of a given ...

A rooted graph is a graph in which one node is labeled in a special way so as to distinguish it from other nodes. The special node is called the root of the graph. The rooted ...