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On Combining the Methods of Link Residual and Domination in Networks

Turacı Tufan

Fundamenta Informaticae

2020

Vol. 174, nr 1

43--59

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 γLR(G), and the average lower link residual domination number, denoted by γLRaν(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.

Combining the Concepts of Residual and Domination in Graphs

Turacı Tufan, Aytaç Aysun

Fundamenta Informaticae

2019

Vol. 166, nr 4

379--392

Let G = (V (G), E(G)) be a simple undirected graph. The domination and average lower domination numbers are vulnerability parameters of a graph. We have investigated a refinement that involves the residual domination and average lower residual domination numbers of these parameters. The lower residual domination number, denoted by γvkR(G), is the minimum cardinality of dominating set in G that received from the graph G where the vertex vk and all links of the vertex vk are deleted. The residual domination number of graphs G is defined as [formula]. The average lower residual domination number of G is defined by [formula]. In this paper, we define the residual domination and the average lower residual domination numbers of a graph and we present the exact values, upper and lower bounds for some graph families.