Domination in signed graphs

Abstract

Let [Formula: see text] be a graph. A signed graph is an ordered pair [Formula: see text] where [Formula: see text] is a graph called the underlying graph of [Formula: see text] and [Formula: see text] is a function called a signature or signing function. Motivated by the innovative paper of B. D. Acharya on domination in signed graphs, we consider another way of defining the concept of domination in signed graphs which looks more natural and has applications in social science. A subset [Formula: see text] of [Formula: see text] is called a dominating set of [Formula: see text] if [Formula: see text] for all [Formula: see text]. The domination number of [Formula: see text], denoted by [Formula: see text], is the minimum cardinality of a dominating set of [Formula: see text]. Also, a dominating set [Formula: see text] of [Formula: see text] with [Formula: see text] is called a [Formula: see text]-set of [Formula: see text]. In this paper, we initiate a study on this parameter.