Some results on majority bad number

Abstract

A two-valued function [Formula: see text] defined on the vertices of a graph [Formula: see text] is a majority bad dominating function (MBDF), if the sum of its function values over at least half the closed neighborhoods is at most one. That is, for at least half the vertices [Formula: see text], [Formula: see text], where [Formula: see text] consists of v and every vertex adjacent to v. The majority bad domination number of a graph G, is denoted by [Formula: see text], and is defined as [Formula: see text]. In this paper, we determine some results on majority bad number.