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Reduced zero-divisor graphs of posets | ||
| Transactions on Combinatorics | ||
| مقاله 5، دوره 7، شماره 2، شهریور 2018، صفحه 47-54 اصل مقاله (233.04 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2018.55164.1417 | ||
| نویسندگان | ||
| Deiborlang Nongsiang* ؛ Promode Kumar Saikia | ||
| North Eastern Hill University | ||
| چکیده | ||
| This paper investigates properties of the reduced zero-divisor graph of a poset. We show that a vertex is an annihilator prime ideal if and only if it is adjacent to all other annihilator prime ideals and there are always two annihilator prime ideals which are not adjacent to a non-annihilator prime ideal. We also classify all posets whose reduced zero-divisor graph is planar or toroidal and the number of distinct annihilator prime ideals is four or seven. | ||
| کلیدواژه‌ها | ||
| poset؛ reduced zero-divisor graph؛ annihilator prime ideal | ||
| مراجع | ||
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[9] A. T. White, Graphs, groups and surfaces, North-Holland Mathematics Studies, no. 8., American Elsevier Publishing Co., Inc., New York, 1973. | ||
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