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Subgroup intersection graph of finite abelian groups | ||
Transactions on Combinatorics | ||
مقاله 2، دوره 1، شماره 3، آذر 2012، صفحه 5-10 اصل مقاله (462.71 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22108/toc.2012.1864 | ||
نویسندگان | ||
T. Tamizh Chelvam* ؛ M. Sattanathan | ||
Manonmaniam Sundaranar University | ||
چکیده | ||
Let $G$ be a finite group with the identity $e$. The subgroup intersection graph $\Gamma_{SI}(G)$ of $G$ is the graph with vertex set $V(\Gamma_{SI}(G)) = G-e$ and two distinct vertices $x$ and $y$ are adjacent in $\Gamma_{SI}(G)$ if and only if $|\left\langle x\right\rangle \cap\left\langle y\right\rangle|>1$, where $\left\langle x\right\rangle $ is the cyclic subgroup of $G$ generated by $x\in G$. In this paper, we obtain a lower bound for the independence number of subgroup intersection graph. We characterize certain classes of subgroup intersection graphs corresponding to finite abelian groups. Finally, we characterize groups whose automorphism group is the same as that of its subgroup intersection graph. | ||
کلیدواژهها | ||
subgroup intersection graph؛ finite abelian groups؛ Independence number | ||
مراجع | ||
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T. Tamizh Chelvam and M. Sattanathan (2011) Subgroup intersection graph of a group J. Adv. Research in Pure Math. (doi:10.5373/ jarpm .594.100910, ISSN:1943-2380). 3 (4), 44-49
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