Some diameter notions in lexicographic product of graphs

Abstract

Many graphs such as hypercubes, star graphs, pancake graphs, grids, tori etc are known to be good interconnection network topologies. In any network topology, the vertices represent the processors and the edges represent links between the processors. Two most important criteriaefficiency and reliability of network models-can be studied with the help of graph theoretical techniques. The lexicographic product is a well studied graph product. The distance notions such as various diameters of a graph help to analyze the efficiency of any interconnection network. In this paper, we study some distance notions such as wide diameter, diameter variability and diameter vulnerability of lexicographic products that could be used in the design of interconnection networks.

Determining the robustness of an interdependent network with a hypergraph model

“…Because of existing a lot of complex interdependencies, prediction of cascading failures in such networks are very difficult. Recently significant efforts have been made in studying and analyzing interdependencies in multi-layered networks [4,5,7,8,9,10,12,13,15,16]. Papers by Rosato [12] and Rinaldi [11] described the concept of interdependency but non of them proposed a mathematical model for deliberation of such networks.…”