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A graph associated to proper non-small subsemimodules of a semimodule | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 12، شماره 2، بهمن 2021، صفحه 499-509 اصل مقاله (381.78 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.5091 | ||
| نویسنده | ||
| Ahmed H. Alwan* | ||
| Department of Mathematics, College of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, Iraq | ||
| تاریخ دریافت: 15 اسفند 1399، تاریخ بازنگری: 04 اردیبهشت 1400، تاریخ پذیرش: 20 اردیبهشت 1400 | ||
| چکیده | ||
| Let M be a unitary left R-semimodule where R is a commutative semiring with identity. The small intersection graph G(M) of a semimodule M is an undirected simple graph with all non-small proper subsemimodules of M as vertices and two distinct vertices N and L are adjacent if and only if N ∩ L is not small in M. In this paper, we investigate the fundamental properties of these graphs to relate the combinatorial properties of G(M) to the algebraic properties of the R-semimodule M. Determine the diameter and the girth of G(M). Moreover, we study cut vertex, clique number, domination number and independence number of the graph G(M). It is shown that the independence number of small graph is equal to the number of its maximal subsemimodules. | ||
| کلیدواژه‌ها | ||
| subsemimodule؛ small intersection graph؛ clique number؛ domination number؛ independence number | ||
| مراجع | ||
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