On global defensive k-alliances in zero-divisor graphs of finite commutative rings

Abstract

The global defensive [Formula: see text]-alliance is a very well-studied notion in graph theory, it provides a method of classification of graphs based on relations between members of a particular set of vertices. In this paper, we explore this notion in zero-divisor graph of commutative rings. The established results generalize and improve recent work by Muthana and Mamouni who treated a particular case for [Formula: see text] known by the global defensive alliance. Various examples are also provided which illustrate and delimit the scope of the established results.