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 t; V, where N(v) is the open neighborhood of v and g(N(v)) = g(u). The weight of iW(v) g is defined by <?(V) = g(u). The minimum weight of a u&V majority total dominating function of G is called the majority total domination number of G and is denoted by In this paper we determine 7for several classes of graphs. We also present bounds for Jmaji) and investigate extremal graphs which attain the bounds. © 2020 Utilitas Mathematica Publishing Inc.. All rights reserved.