Majority bad number
S. Anandha Prabhavathy · Discrete Mathematics Algorithms and Applications · 2020
A two-valued function [Formula: see text] defined on the vertices of a graph [Formula: see text] is a majority bad dominating function, briefly (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 [Formula: see text] and every vertex adjacent to [Formula: see text]. The majority bad domination number of a graph [Formula: see text] is denoted by [Formula: see text] and is defined as [Formula: see text]. In this paper, we initiate the study of majority bad number in graphs.