- Tytuł:
- Self-coalition graphs
- Autorzy:
-
Haynes, Teresa W.
Hedetniemi, Jason T.
Hedetniemi, Stephen T.
McRae, Alice A.
Mohan, Raghuveer - Powiązania:
- https://bibliotekanauki.pl/articles/29519279.pdf
- Data publikacji:
- 2023
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
coalitions in graphs
coalition partitions
coalition graphs
domination - Opis:
- 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 ∪ V_2 $ is a dominating set of $ G $. A coalition partition in a graph $ G $ of order $ n = |V| $ is a vertex partition $ π = {V_1, V_2, . . . , 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 $ π $ of a graph $ G $ is a graph called the coalition graph of $ G $ with respect to $ π $, denoted $ CG(G, π) $, the vertices of which correspond one-to-one with the sets $ V_1, V_2, . . . , V_k $ of $ π $ and two vertices are adjacent in $ CG(G, π) $ if and only if their corresponding sets in $ π $ form a coalition. The singleton partition $ π_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, π_1)$, where $π_1$ is the singleton partition of $ G $. In this paper, we characterize self-coalition graphs.
- Źródło:
-
Opuscula Mathematica; 2023, 43, 2; 173-183
1232-9274
2300-6919 - Pojawia się w:
- Opuscula Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł