Combining the Concepts of Residual and Domination in Graphs


FUNDAMENTA INFORMATICAE, cilt.166, ss.379-392, 2019 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 166 Konu: 4
  • Basım Tarihi: 2019
  • Doi Numarası: 10.3233/fi-2019-1806
  • Sayfa Sayıları: ss.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 gamma(R)(uk)(G), is the minimum cardinality of dominating set in G that received from the graph G where the vertex v(k) and all links of the vertex v(k) are deleted. The residual domination number of graphs G is defined as gamma(R)(G) = minv(k)is an element of V(G){gamma(R)(vk)(G)} . The average lower residual domination number of G is de- fined by gamma(R)(av)(G) = 1/vertical bar V(G)vertical bar Sigma(vk is an element of V(G)) gamma(R)(vk)(G). 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.