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A double-toroidal graph is a graph with graph genus 2 (West 2000, p. 266). Planar and toroidal graphs are therefore not double-toroidal. Some known double-toroidal graphs on ...

A lobster graph, lobster tree, or simply "lobster," is a tree having the property that the removal of leaf nodes leaves a caterpillar graph (Gallian 2007). The numbers of ...

An edge coloring of a graph G is a coloring of the edges of G such that adjacent edges (or the edges bounding different regions) receive different colors. An edge coloring ...

A trail is a walk v_0, e_1, v_1, ..., v_k with no repeated edge. The length of a trail is its number of edges. A u,v-trail is a trail with first vertex u and last vertex v, ...

There exists no known P algorithm for graph isomorphism testing, although the problem has also not been shown to be NP-complete. In fact, the problem of identifying ...

The Hamiltonian number h(n) of a connected graph G is the length of a Hamiltonian walk G. In other words, it is the minimum length of a closed spanning walk in the graph. For ...

The Hochberg-O'Donnell fish graph is the unit-distance graph on 23 nodes and 42 edges illustrated above. It is triangle-free and is the smallest example of a unit-distance ...

The Tutte 8-cage (Godsil and Royle 2001, p. 59; right figure) is a cubic graph on 30 nodes and 45 edges which is the Levi graph of the Cremona-Richmond configuration. It ...

A tree not having the complete bipartite graph K_(1,2) with base at the vertex of degree two as a limb (Lu et al. 1993, Lu 1996).

A graph G is fully reconstructible in C^d if the graph is determined from its d-dimensional measurement variety. If G is globally rigid in R^d on n>=d+2 vertices, then G is ...