2023/02/21 by Nazli Besharati, Doost Ali Mojdeh, Mojdeh, Doost Ali +4 · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #math.CO
paper · pdf · doi:10.48550/arxiv.2302.10926
arxiv created 2026/07/30 · arxiv updated 2026/08/03
An edge coalition in a graph G=(V,E) consists of two disjoint sets of edges E1 and E2, neither of which is an edge dominating set but whose union E1∪ E2 is an edge dominating set. An edge coalition partition in a graph G of order n=|V| and size m is an edge partition π=\E1,⋯,Ek\ so that every set Ei of π either is a singleton edge dominating set, or is not an edge dominating set but forms an edge coalition with another set Ej which is not an edge dominating set. In this paper we introduce the concept of edge coalition and show that there exists edge coalition for some graphs and trees. The graphs G with small and size number of edge coalition are characterized. Finally, coalition graphs of special graphs are studied.