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arXiv · 2107.08418

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

Driss Bennis·Brahim El Alaoui·Khalid Ouarghi
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Abstract

The global defensive $k$-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 $k=-1$ known by the global defensive alliance. Various examples are also provided which illustrate and delimit the scope of the established results.

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Driss Bennis, Brahim El Alaoui, Khalid Ouarghi. 2021-07-18. On global defensive k-alliances in zero-divisor graph of finite commutative rings. https://arxiv.org/abs/2107.08418

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