TY - JOUR ID - 14328 TI - On perfectness of annihilating-ideal graph of $\mathbb{Z}_n$ JO - Communications in Combinatorics and Optimization JA - CCO LA - en SN - 2538-2128 AU - Saha, Manideepa AU - Biswas, Sucharita AU - Das, Angsuman AD - Presidency University, Kolkata AD - Department of Mathematics, Presidency University, Kolkata Y1 - 2023 PY - 2023 VL - 8 IS - 1 SP - 173 EP - 181 KW - annihilator KW - perfect graph KW - ideals DO - 10.22049/cco.2021.27382.1252 N2 - The annihilating-ideal graph of a commutative ring $R$ with unity is defined as the graph $AG(R)$ whose vertex set is the set of all non-zero ideals with non-zero annihilators and two distinct vertices $I$ and $J$ are adjacent if and only if $IJ = 0$. Nikandish et.al. proved that $AG(\mathbb{Z}_n)$ is weakly perfect. In this short paper, we characterize $n$ for which $AG(\mathbb{Z}_n)$ is perfect. UR - http://comb-opt.azaruniv.ac.ir/article_14328.html L1 - http://comb-opt.azaruniv.ac.ir/article_14328_df3f829c2e7dfbee3bdc028abc687ae5.pdf ER -