Total domination in graphs

Abstract

A set D of vertices of a finite, undirected graph C = ( V , E) is a total dominating set if every vertex of Y is adjacent to some vertex of D. In this paper we initiate the study of total dominating sets in graphs and, in particular, obtain results concerning the total domination number of G (the smallest number of vertices in a total dominating set) and the total domatic number of C (the largest order of a partition of C into total dominating sets).

γ-total dominating graphs of paths and cycles

“…A set D of vertices in a graph G is called a total dominating set if every vertex of G is adjacent to some vertex in D. Total dominating sets were introduced by Cockayne et al 9 .…”

Some Domination Parameters of Arithmetic Graph Vn

“…Total dominating sets are introduced by Cockayane, Dawes and Hedetniemi [7]. Some results regarding total domination can be seen in [ 8 ].…”

An upper bound on the total outer-independent domination number of a tree

“…A subset D ⊆ V (G) is a dominating set of G if every vertex of V (G) \ D has a neighbor in D, while it is a total dominating set if every vertex of G has a neighbor in D. The domination (total domination, respectively) number of G, denoted by γ(G) (γ t (G), respectively), is the minimum cardinality of a dominating (total dominating, respectively) set of G. Total domination in graphs was introduced by Cockayne, Dawes, and Hedetniemi [2], and further studied for example in [1]. For a comprehensive survey of domination in graphs, see [3,4].…”