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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.