Differentiating total dominating sets in the join, corona and composition of graphs
Benjamin N. Omamalin, Sergio R. Canoy, Helen Moso Rara · International Journal of Mathematical Analysis · 2014
Let G =( V (G), E(G)) be a connected graph. A subset S of V (G )i s a total dominating set of G if every vertex of G is adjacent to some vertex in S. The set NG(v) is the set of all vertices of G adjacent to v including v. A subset S of V (G) is a differentiating set of G if NG(u)∩SNG(v)∩S for every two distinct vertices u and v in V (G). A differentiating subset S of V (G) which is also total dominating is called a differentiating total dominating set of G. The minimum cardinality of a differentiating total dominating set of G is called the differentiating total domination number of G. In this paper we characterize the differentiating total dominating sets in the join, corona and composition of graphs. Mathematics Subject Classification: 05C69