Coalition Graphs
چکیده(به انگلیسی؛ چکیدهی فارسی در دسترس نیست)
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 $V_j$. 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. In this paper, we initiate the study of coalition graphs and we show that every graph is a coalition graph.
نویسندگان و وابستگی سازمانی
- Teresa Haynes — East Tennessee State University; Department of Mathematics University of Johannesburg
- Jason Hedetniemi — Florida Atlantic University
- Stephen Hedetniemi — Professor Emeritus Clemson University Clemson, South Carolina
- Alice McRae — Appalachian State University
- Raghuveer Mohan — Appalachian State University