In this paper, we study the connectivity of the complement of a graph. We first establish a simple formula to compute the connectivity of a graph that comes from the join of graphs. Base on this formula, we give an upper and a lower bound to the connectivity of the complement of a graph. Keyword: connectivity, complement, join, vertex of attachment.

The relationship between graph coloring and the immersion order is considered. Vertex connectivity, edge connectivity and related issues are explored. These lead to the conjecture that, if G requires at least t colors, then G must have immersed within it Kt, the complete graph on t vertices. Evidence in support of such a proposition is presented. For each fixed value of t, there can be only a f...

Let x be a vertex of a simple graph G. The vertex-type of x is the lexicographically ordered degree sequence of its neighbors. We call the graph G vertex-oblique if there are no two vertices in V (G) which are of the same vertex-type. We will show that the set of vertex-oblique graphs of arbitrary connectivity is infinite. © 2006 Elsevier B.V. All rights reserved.

Delphi is a new geometry-guided predictive compression scheme for squeezing the connectivity of a triangluar mesh. The mesh is traversed using the Edgebreaker state machine. Instead of creating the Edgebreaker clers sequence both compression and decompression perform the same geometric prediction of the location of the unknown vertex of the next triangle during the mesh traversal. Based on this...

A scan statistic methodology for detecting anomalies has been developed for application to graphs. We equate anomalies with vertices that exhibit high local connectivity properties. In particular we look for cases where all vertices have similar local connectivity, except for one vertex (a champion) that has much higher connectivity at a certain level. For example, a neighborhood champion is a ...

Given an undirected graph G and a positive integer k, the k-vertex-connectivity augmentation problem is to find a smallest set F of new edges for which G + F is k-vertex-connected. Polynomial algorithms for this problem have been found only for k≤ 4 and a major open question in graph connectivity is whether this problem is solvable in polynomial time in general. In this paper we develop an algo...

These lecture notes are on automorphism groups of Cayley graphs and their applications to optimal fault-tolerance of some interconnection networks. We first give an introduction to automorphisms of graphs and an introduction to Cayley graphs. We then discuss automorphism groups of Cayley graphs. We prove that the vertex-connectivity of edge-transitive graphs is maximum possible. We investigate ...