A central issue in the analysis of complex networks is the assessment of their robustness and vulnerability. A variety of measures have been proposed in the literature to quantify the robustness of networks and a number of graph-theoretic parameters have been used to derive formulas for calculating network reliability. In this paper, we study the vulnerability of interconnection networks to the failure of individual nodes, using a graph-theoretic concept of residual closeness as a measure of network robustness which provides a much fuller characterization of the network.
Robustness of the network topology is a key aspect in the design of computer networks. Vertex residual closeness is a new graph-theoretic concept defined as a measure of network robustness. In this model, edges are perfectly reliable and the vertices fail independently of each other. In this paper, vertex residual closeness of paths and regular caterpillars are calculated by giving an insight of how to evaluate the vertex residual closeness of path-like graphs.
Link residual closeness is reported as a new graph vulnerability measure, a graph-based approach to network vulnerability analysis, and more sensitive than some other existing vulnerability measures. Residual closeness is of great theoretical and practical significance to network design and optimization. In this paper, how some of the graph types perform when they suffer a link failure is discussed. Vulnerability of graphs to the failure of individual links is computed via link residual closeness which provides a much fuller characterization of the network.
Link residual closeness is a novel graph based network vulnerability parameter. In this model, nodes are perfectly reliable and the links fail independently of each other. In this paper, the behavior of composite network types to the failure of individual links are observed and analyzed via link residual closeness which provides a much fuller characterization of the network.
Let G = (V,E) be a graph of order n and let B(D) be the set of vertices in V \ D
that have a neighbor in the vertex set D . The differential of a vertex set D is defined as
( ) ( ) D B D D = − and the maximum value of ( ) D for any subset D of V is the
differential of G . A set D of vertices of a graph G is said to be a dominating set if every
vertex in \ V D is adjacent to a vertex in D . G is a dominant differential graph if it contains
a -set which is also a dominating set. This paper is devoted to the computation of
differential of wheel, cycle and path-related graphs as infrastructure networks. Furthermore,
dominant differential wheel, cycle and path-related types of networks are recognized.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.