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On the anti-forcing number of graph powers | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 8، دوره 9، شماره 3، آذر 2024، صفحه 497-507 اصل مقاله (3.47 M) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2023.27874.1378 | ||
| نویسندگان | ||
| Neda Soltani؛ Saeid Alikhani* | ||
| Department of Mathematical Sciences, Yazd University, 89195-741, Yazd, Iran | ||
| چکیده | ||
| Let $G=(V,E)$ be a simple connected graph. A perfect matching (or Kekul'e structure in chemical literature) of $G$ is a set of disjoint edges which covers all vertices of $G$. The anti-forcing number of $G$ is the smallest number of edges such that the remaining graph obtained by deleting these edges has a unique perfect matching and is denoted by $af(G)$. For every $m\in\mathbb{N}$, the $m$th power of $G$, denoted by $G^m$, is a graph with the same vertex set as $G$ such that two vertices are adjacent in $G^m$ if and only if their distance is at most $m$ in $G$. In this paper, we study the anti-forcing number of the powers of some graphs. | ||
| کلیدواژهها | ||
| perfect matching؛ anti-forcing number؛ power of a graph | ||
| مراجع | ||
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