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.
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Tamizh Chelvam, T. and Sattanathan, M. (2012). Subgroup intersection graph of finite abelian groups. Transactions on Combinatorics, 1(3), 5-10. doi: 10.22108/toc.2012.1864
MLA
Tamizh Chelvam, T. , and Sattanathan, M. . "Subgroup intersection graph of finite abelian groups", Transactions on Combinatorics, 1, 3, 2012, 5-10. doi: 10.22108/toc.2012.1864
HARVARD
Tamizh Chelvam, T., Sattanathan, M. (2012). 'Subgroup intersection graph of finite abelian groups', Transactions on Combinatorics, 1(3), pp. 5-10. doi: 10.22108/toc.2012.1864
CHICAGO
T. Tamizh Chelvam and M. Sattanathan, "Subgroup intersection graph of finite abelian groups," Transactions on Combinatorics, 1 3 (2012): 5-10, doi: 10.22108/toc.2012.1864
VANCOUVER
Tamizh Chelvam, T., Sattanathan, M. Subgroup intersection graph of finite abelian groups. Transactions on Combinatorics, 2012; 1(3): 5-10. doi: 10.22108/toc.2012.1864
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