Secure equitable domination in Cartesian product of graphs

In graphs, several domination parameters have been introduced by incorporating a combination of the existing ones. A secure equitable domination is a domination in which the dominating set admits the properties of both; secure as well as equitable dominating sets. An equitable dominating set [Formula: see text] of a graph [Formula: see text] is said to be secure equitable dominating set, if for every [Formula: see text], there exists a vertex [Formula: see text] such that [Formula: see text] and [Formula: see text] are adjacent and [Formula: see text] is an equitable dominating set of [Formula: see text]. The minimum cardinality of a secure equitable dominating set of [Formula: see text] is called the secure equitable domination number of [Formula: see text]. In this paper, we study certain cases were the secure domination, the equitable domination and the secure equitable domination bounds are equal. Moreover, we establish the bounds of secure equitable domination number of the Cartesian product of graphs.