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Line graph characterization of the order supergraph of a finite group | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 31 مرداد 1403 اصل مقاله (543.39 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.29375.1962 | ||
| نویسندگان | ||
| Manisha Manisha؛ Parveen Parveen؛ Jitender Kumar* | ||
| Department of Mathematics, Birla Institute of Technology and Science Pilani, Pilani-333031, India | ||
| چکیده | ||
| The power graph ${\mathcal{P}(G)}$ is the simple undirected graph with group elements as a vertex set and two elements are adjacent if one of them is a power of the other. The order supergraph ${\mathcal{S}(G)}$ of the power graph ${\mathcal{P}(G)}$ is the simple undirected graph with vertex set $G$ in which two vertices $x$ and $y$ are adjacent if $o(x)\vert o(y)$ or $o(y)\vert o(x)$. In this paper, we classify all the finite groups $G$ such that the order supergraph ${\mathcal{S}(G)}$ is the line graph of some graph. Moreover, we characterize finite groups whose order supergraphs are the complement of line graphs. | ||
| کلیدواژه‌ها | ||
| Power graph؛ order supergraph of power graph؛ line graph؛ finite groups؛ EPPO-group | ||
| مراجع | ||
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