On global offensive k-alliances in graphs

TL;DR

This paper explores the properties of global offensive k-alliances in graphs, establishing bounds on their size based on various graph parameters, and relating them to other characteristic sets.

Contribution

It introduces new bounds on the global offensive k-alliance number by connecting it with r-dependent and τ-dominating sets, advancing theoretical understanding.

Findings

Derived bounds on global offensive k-alliance number

Linked alliance properties with r-dependent and τ-dominating sets

Enhanced theoretical framework for graph alliances

Abstract

We investigate the relationship between global offensive $k$-alliances and some characteristic sets of a graph including $r$-dependent sets and $\tau$-dominating sets. As a consequence of the study, we obtain bounds on the global offensive $k$-alliance number in terms of several parameters of the graph.