Vulnerability of Mycielski Graphs via Residual Closeness

Abstract

The vulnerability value of a communication network is the resistance of this communication network until some certain stations or communication links between these stations are disrupted and, thus communication interrupts. A communication network is modeled by a graph to measure the vulnerability as stations corresponding to the vertices and communication links corresponding to the edges, There are several types of vulnerability parameters depending upon the distance for each pair of two vertices. In this paper. closeness, vertex residual closeness ($VRC$) and normalized vertex residual closeness ($NVRC$) of some Mycielski graphs are calculated, furthermore upper and lower bounds are obtained.