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Some algebraic properties of the subdivision graph of a graph | ||
Communications in Combinatorics and Optimization | ||
مقاله 10، دوره 9، شماره 2، شهریور 2024، صفحه 297-307 اصل مقاله (413.04 K) | ||
نوع مقاله: Original paper | ||
شناسه دیجیتال (DOI): 10.22049/cco.2023.28270.1494 | ||
نویسنده | ||
Seyed Morteza Mirafzal* | ||
Department of Mathematics, Faculty of Basic Sciences, Lorestan University, Khorramabad, Iran | ||
چکیده | ||
Let $G=(V,E)$ be a connected graph with the vertex-set $V$ and the edge-set $E$. The subdivision graph $S(G)$ of the graph $G$ is obtained from $G$ by adding a vertex in the middle of every edge of $G$. In this paper, we investigate some properties of the graphs $S(G)$ and $L(S(G))$, where $L(S(G))$ is the line graph of $S(G)$. We will see that $S(G)$ and $L(S(G))$ inherit some properties of $G$. For instance, we show that if $G \ncong C_n$, then $Aut(G) \cong Aut(L(S(G)))$ (as abstract groups), where $C_n$ is the cycle of order $n$. | ||
کلیدواژهها | ||
subdivision graph؛ line graph؛ connectivity؛ automorphism group؛ hamiltonian graph | ||
مراجع | ||
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