Dutta, S., Lanong, C. (2017). On annihilator graph of a finite commutative ring. Transactions on Combinatorics, 6(1), 1-11. doi: 10.22108/toc.2017.20360

Sanghita Dutta; Chanlemki Lanong. "On annihilator graph of a finite commutative ring". Transactions on Combinatorics, 6, 1, 2017, 1-11. doi: 10.22108/toc.2017.20360

Dutta, S., Lanong, C. (2017). 'On annihilator graph of a finite commutative ring', Transactions on Combinatorics, 6(1), pp. 1-11. doi: 10.22108/toc.2017.20360

Dutta, S., Lanong, C. On annihilator graph of a finite commutative ring. Transactions on Combinatorics, 2017; 6(1): 1-11. doi: 10.22108/toc.2017.20360

The annihilator graph $AG(R)$ of a commutative ring $R$ is a simple undirected graph with the vertex set $Z(R)^*$ and two distinct vertices are adjacent if and only if $ann(x) \cup ann(y)$ $ \neq $ $ann(xy)$. In this paper we give the sufficient condition for a graph $AG(R)$ to be complete. We characterize rings for which $AG(R)$ is a regular graph, we show that $\gamma (AG(R))\in \{1,2\}$ and we also characterize the rings for which $AG(R)$ has a cut vertex. Finally we find the clique number of a finite reduced ring and characterize the rings for which $AG(R)$ is a planar graph.

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