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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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[10] S.M. Mirafzal, A new class of integral graphs constructed from the hypercube, Linear Algebra Appl. 558 (2018), 186–194. https://doi.org/10.1016/j.laa.2018.08.027 [11] S.M. Mirafzal, The automorphism group of the bipartite Kneser graph, Proc. Math. Sci. 129 (2019), Article number 34. https://doi.org/10.1007/s12044-019-0477-9 [12] S.M. Mirafzal, On the automorphism groups of connected bipartite irreducible graphs, Proc. Math. Sci. 130 (2020), Article number 57. https://doi.org/10.1007/s12044-020-00589-1 [13] S.M. Mirafzal, Cayley properties of the line graphs induced by consecutive layers of the hypercube, Bull. Malays. Math. Sci. Soc. 44 (2021), 1309–1326. https://doi.org/10.1007/s40840-020-01009-3 [14] S.M. Mirafzal, A note on the automorphism groups of Johnson graphs, Ars Combin. 154 (2021), 245–255.
[15] S.M. Mirafzal, Some remarks on the square graph of the hypercube, Ars Math. Contemp. 23 (2023), no. 2, #P2.06 https://doi.org/10.26493/1855-3974.2621.26f [16] S.M. Mirafzal and A. Zafari, Some algebraic properties of bipartite Kneser graphs, Ars Combin. 153 (2020), 3–12.
[17] S.M. Mirafzal and M. Ziaee, A note on the automorphism group of the Hamming graph, Trans. Comb. 10 (2021), no. 2, 129–136. https://doi.org/10.22108/toc.2021.127225.1817 [18] G. Sabidussi, Vertex-transitive graphs, Monatsh. Math. 68 (1964), 426–438. | ||
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