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On the complement of the intersection graph of subgroups of a group | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 3، دوره 10، شماره 1، خرداد 2025، صفحه 57-68 اصل مقاله (762.12 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2023.28198.1476 | ||
| نویسندگان | ||
| P. Devi1؛ R. Rajkumar* 2 | ||
| 1Department of Mathematics, Sri Paramakalyani College, Alwarkurichi - 627 412, Tamil Nadu, India. | ||
| 2Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram - 624 302, Tamil Nadu, India | ||
| چکیده | ||
| The complement of the intersection graph of subgroups of a group $G$, denoted by $\mathcal{I}^c(G)$, is the graph whose vertex set is the set of all nontrivial proper subgroups of $G$ and its two distinct vertices $H$ and $K$ are adjacent if and only if $H\cap K$ is trivial. In this paper, we classify all finite groups whose complement of the intersection graph of subgroups is one of totally disconnected, bipartite, complete bipartite, tree, star graph or $C_3$-free. Also we characterize all the finite groups whose complement of the intersection graph of subgroups is planar. | ||
| کلیدواژه‌ها | ||
| complement of intersection graph of subgroups؛ bipartite graph؛ planar graph | ||
| مراجع | ||
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