The Characterizations of Hinge-free Networks.

Abstract

In this paper, a graph representation model of the reliable network designs is presented. A graph is said to be hinge-free if the removal of any single vertex in the graph results in no increase in distance between any two remaining vertices. The advantages of the proposed structure are not only residual connectedness related to the class of hinge-free graphs and its generalization, called the k-GC graphs ( a class of connected graphs by removing at least k vertices is required to increase the distance between any two remaining vertices), established .Base on this property, we show that all the above classes of graphs can be recognized in O(｜V∣∣E∣) time in spite of the value of k. We also provide some extensions of graphs with respect to the hinge-free property (resp. k-GC property) such that a hinge-free (resp. k-GC) network on large scale can easily be constructed by using these operations. Finally, the relationships among hinge-free graphs and other classes of graphs are discussed.