Domination changing and unchanging signed graphs upon the vertex removal

Abstract

A subset S of V (Σ) is a dominating set of Σ if |N⁺(v) ∩ S| > |N⁻(v) ∩ S| for all v ∈ V − S. This article is to start a study of those signed graphs that are stable and critical in the following way: If the removal of an arbitrary vertex does not change the domination number, the signed graph will be stable. The signed graph, on the other hand, is unstable if an arbitrary vertex is removed and the domination number changes. Specifically, we analyze the change in the domination of the vertex deletion and stable signed graphs.Publisher's Versio