TY - JOUR
ID - 1864
TI - Subgroup intersection graph of finite abelian groups
JO - Transactions on Combinatorics
JA - TOC
LA - en
SN - 2251-8657
AU - Tamizh Chelvam, T.
AU - Sattanathan, M.
AD - Manonmaniam Sundaranar University
Y1 - 2012
PY - 2012
VL - 1
IS - 3
SP - 5
EP - 10
KW - subgroup intersection graph
KW - finite abelian groups
KW - Independence number
DO - 10.22108/toc.2012.1864
N2 - 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.
UR - https://toc.ui.ac.ir/article_1864.html
L1 - https://toc.ui.ac.ir/article_1864_bfb49638f7dc2dacb195f5bcbbe3091f.pdf
ER -