Introduction to Coalitions in Graphs
A coalition in a graph (Formula presented.) consists of two disjoint sets of vertices V 1 and V 2, neither of which is a dominating set but whose union (Formula presented.) is a dominating set. A coalition partition in a graph G of order (Formula presented.) is a vertex partition (Formula presented.) such that every set Vi of π either is a dominating set consisting of a single vertex of degree n–1, or is not a dominating set but forms a coalition with another set (Formula presented.) which is not a dominating set. In this paper we introduce this concept and study its properties.
Haynes, Teresa W.; Hedetniemi, Jason T.; Hedetniemi, Stephen T.; McRae, Alice A.; and Mohan, Raghuveer. 2020. Introduction to Coalitions in Graphs. AKCE International Journal of Graphs and Combinatorics. Vol.17(2). 653-659. https://doi.org/10.1080/09728600.2020.1832874 ISSN: 0972-8600