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A Simple-Intersection Graph of a Ring Approach to Solving Coloring Optimization Problems | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 19 آذر 1402 اصل مقاله (413.73 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2023.28858.1752 | ||
| نویسندگان | ||
| Fida Moh'd؛ Mamoon Ahmed* | ||
| Department of Basic Sciences, Princess Sumaya University for Technology, Amman, Jordan | ||
| چکیده | ||
| In this paper, we introduce a modified version of the simple-intersection graph for semisimple rings, applied to a ring $R$ with unity. The findings from this modified version are subsequently utilized to solve several coloring optimization problems. We demonstrate how the clique number of the simple-intersection graph can be used to determine the maximum number of possibilities that can be selected from a set of $n$ colors without replacement or order, subject to the constraint that any pair shares only one common color. We also show how the domination number can be used to determine the minimum number of possibilities that can be selected, such that any other possibility shares one color with at least one of the selected possibilities, is $n-1$. | ||
| کلیدواژه‌ها | ||
| Simple-intersection graph؛ semisimple rings؛ ideals؛ cliques؛ girth | ||
| مراجع | ||
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