Affiliation:
1. Department of Mathematics, College of Education for Pure Sciences, Thi-Qar University, Thi-Qar, Iraq
Abstract
Let [Formula: see text] be a finite graph, simple, undirected and has no isolated vertex. A dominating subset [Formula: see text] of [Formula: see text] is said a bi-dominating set, if every vertex of it dominates two vertices of [Formula: see text]. The bi-domination number of [Formula: see text], denoted by [Formula: see text] is the minimum cardinality over all bi-dominating sets in [Formula: see text]. In this paper, a certain modified bi-domination parameter called doubly connected bi-domination and its inverse are introduced. Several bounds and properties are studied here. These modified dominations are applied and evaluated for several well-known graphs and complement graphs.
Publisher
World Scientific Pub Co Pte Lt
Subject
Discrete Mathematics and Combinatorics
Cited by
13 articles.
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