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The average disorder number of a simple connected graph on n vertices is defined as the average length of a walk along the edges of the graph taken over all ordering of its ...

Let G be a k-regular graph with girth 5 and graph diameter 2. (Such a graph is a Moore graph). Then, k=2, 3, 7, or 57. A proof of this theorem is difficult (Hoffman and ...

A member of a collection of sets is said to be maximal if it cannot be expanded to another member by addition of any element. Maximal sets are important in graph theory since ...

Given a collection of sets, a member set that is not a proper subset of another member set is called a minimal set. Minimal sets are important in graph theory, since many ...

A cycle graph of a group is a graph which shows cycles of a group as well as the connectivity between the cycles. Such graphs are constructed by drawing labeled nodes, one ...

A finite simple connected graph G is quadratically embeddable if its quadratic embedding constant QEC(G) is nonpositive, i.e., QEC(G)<=0. A graph being quadratically ...

A polyhedral graph on five nodes. There are two topologically distinct pentahedral graphs which, through duality, correspond to the skeletons of the square pyramid (left ...

A d-dimensional framework is a pair (G,p) where G=(V,E) is a graph with vertex set V and edge set E and p:V->R^d is a map that assigns a point in R^d to each vertex of G. The ...

The truncated pentakis dodecahedral graph, illustrated above in a pair of embeddings, is the skeleton of the truncated pentakis dodecahedron. It has 180 vertices, 270 edges, ...

Consider a broadcast scheme on a connected graph from an originator vertex v in a graph G consisting of a sequence of parallel calls starting from v. In each time step, every ...