University of IsfahanTransactions on Combinatorics2251-86571320120901Subgroup intersection graph of finite abelian groups510186410.22108/toc.2012.1864ENT.Tamizh ChelvamManonmaniam Sundaranar University0000-0002-1878-7847M.SattanathanManonmaniam Sundaranar UniversityJournal Article20120916Let $G$ 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.https://toc.ui.ac.ir/article_1864_bfb49638f7dc2dacb195f5bcbbe3091f.pdf