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- W4361000216 abstract "A coalition in a graph (G = (V, E)) consists of two disjoint sets (V_1) and (V_2) of vertices, such that neither (V_1) nor (V_2) is a dominating set, but the union (V_1 cup V_2) is a dominating set of (G). A coalition partition in a graph (G) of order (n = |V|) is a vertex partition (pi = {V_1, V_2, ldots, V_k}) such that every set (V_i) 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 (V_j) which is not a dominating set. Associated with every coalition partition (pi) of a graph (G) is a graph called the coalition graph of (G) with respect to (pi), denoted (CG(G,pi)), the vertices of which correspond one-to-one with the sets (V_1, V_2, ldots, V_k) of (pi) and two vertices are adjacent in (CG(G,pi)) if and only if their corresponding sets in (pi) form a coalition. The singleton partition (pi_1) of the vertex set of (G) is a partition of order (|V|), that is, each vertex of (G) is in a singleton set of the partition. A graph (G) is called a self-coalition graph if (G) is isomorphic to its coalition graph (CG(G,pi_1)), where (pi_1) is the singleton partition of (G). In this paper, we characterize self-coalition graphs." @default.
- W4361000216 created "2023-03-30" @default.
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- W4361000216 date "2023-01-01" @default.
- W4361000216 modified "2023-09-24" @default.
- W4361000216 title "Self-coalition graphs" @default.
- W4361000216 doi "https://doi.org/10.7494/opmath.2023.43.2.173" @default.
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