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On annihilator graph of a finite commutative ring | ||
| Transactions on Combinatorics | ||
| مقاله 1، دوره 6، شماره 1، خرداد 2017، صفحه 1-11 اصل مقاله (249.31 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2017.20360 | ||
| نویسندگان | ||
| Sanghita Dutta* 1؛ Chanlemki Lanong2 | ||
| 1North eastern Hill University | ||
| 2North Eastern Hill University | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Annihilator؛ Clique number؛ Domination Number | ||
| مراجع | ||
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[9] T. T. Chelvam and T. Asir, Domination in the Total Graph on Zn , Discrete Math. Algorithms Appl., 3 no. 4 (2011) 413-421.
[10] D. A. Mo jdeh and A. M. Rahimi, Dominating Sets of Some Graphs Asso ciated to Commutative Rings, Comm. Algebra, 40 no. 9 (2012) 3389-3396. | ||
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