Subgroup intersection graph of finite abelian groups

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|>۱‎, ‎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.

کلیدواژه ها:

subgroup intersection graph ، finite abelian groups ، Independence number