A coalition in a graph consists of two disjoint sets of vertices V1 and V2, neither of which is a dominating set but whose union is a dominating set. A coalition partition in a graph G of order is a vertex partition 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 which is not a dominating set. In this paper we introduce this concept and study its properties.
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Haynes et al. (2020) studied this question.