3-tuple total domination number of rook's graphs

Abstract

A k-tuple total dominating set (kTDS) of a graph G is a set S of vertices in which every vertex in G is adjacent to at least k vertices in S. The minimum size of a kTDS is called the ktuple total dominating number and it is denoted by γ ×k,t (G). We give a constructive proof of a general formula for γ ×3,t (K n K m ).Date: October 1, 2018.

Total domination number of middle graphs

“…The previous two notions play a central role in graph theory and the literature on the subject is vast, see for example [9][10][11], [16], [18] and [19]. Since the introduction of the domination number of a graph, many variation have been introduced.…”

Total domination number of middle graphs

“…The concept of total domination in graph theory was first introduced by Cockayne, Dawes and Hedetniemi in [3] and it has been studied extensively by many researchers in the last years, see for example [5], [6], [7], [13], [8], [10], [12] and [14]. The literature on this subject has been surveyed and detailed in the recent book [7].…”

New classification of graphs in view of the domination number of central graphs

“…The notion of domination and its many generalizations have been intensively studied in graph theory and the literature on this subject is vast, see for example [2], [3], [4], [6], [11] and [13]. Throughout this paper, we use standard notation for graphs and we assume that each graph is finite, undirected and simple.…”