On majority total domination in graphs

Abstract

A majority total dominating function of a graph G = (V, E) is a function g : V {-1,1} such that g(N(v)) > 1 for at least half of the vertices v G V, where N(v) is the open neighborhood of v and g(N(v)) = £ 9(u)-The weight of u N(v) g is defined by (V) = £ 9(u)> The minimum weight of a majority total dominating function of G is called the majority total domination number of G and is denoted by In this paper we determine yj for several classes of graphs. We also present bounds for (G) and investigate extremal graphs which attain the bounds. © 2019 Utilitas Mathematica Publishing Inc.. All rights reserved.