The independent transversal total domination number of some graphs

Abstract

A total dominating set of a graph G having non empty intersection with all the independent sets of maximum cardinality in G is an independent transversal total dominating set. The minimum cardinality of any independent transversal total dominating set is denoted by γtt(G)- In this paper, we mainly study on the bounds of independent transversal total dominating set of graphs, such as graphs with diameter 2, graphs with some special independence number, cographs and -P₄-sparse graphs. Moreover, we list polynomial-time algorithms to compute the independent transversal total dominating numbers of cographs and P₄-sparse graphs. © 2019 Utilitas Mathematica Publishing Inc.. All rights reserved.