On Combining the Methods of Link Residual and Domination in Networks

Abstract

The concept of vulnerability is very important in network analysis. Several existing parameters have been proposed in the literature to measure network vulnerability, such as domination number, average lower domination number, residual domination number, average lower residual domination number, residual closeness and link residual closeness. In this paper, incorporating the concept of the domination number and link residual closeness number, as well as the idea of the average lower domination number, we introduce new graph vulnerability parameters called the link residual domination number, denoted by γ ^LR (G), and the average lower link residual domination number, denoted by ${\gamma }_{av}^{LR}(G)$ , for any given graph G. Furthermore, the exact values and the upper and lower bounds for any graph G are given, and the exact results of well-known graph families are computed.