Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 13 2 2022 07 01 On the co-intersection graph of subsemimodules of a semimodule 2763 2770 6621 10.22075/ijnaa.2022.27521.3637 EN Ahmed H. Alwan Department of Mathematics, College of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, Iraq Zahraa A. Nema Department of Mathematics, College of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, Iraq Journal Article 2022 04 06 Let $S$ be a semiring with identity and $U$ be a unitary left $S$-semimodule. The co-intersection graph of an $S$-semimodule $U$, denoted by $\Gamma(U)$, is defined to be the undirected simple graph whose vertices are in one-to-one correspondence with all non-trivial subsemimodules of $U$, and there is an edge between two distinct vertices $N$ and $L$ if and only if $N+L \neq U$. We study these graphs to relate the combinatorial properties of $\Gamma(U)$ to the algebraic properties of the $S$-semimodule $U$. We study the connectedness of $\Gamma(U)$. We investigate some properties of $\Gamma(U)$ for instance, we find the domination number and clique number of $\Gamma(U)$. Also, we study cycles in $\Gamma(U)$. https://ijnaa.semnan.ac.ir/article_6621_ea84d69753b75af0fe05b36ecfed4c07.pdf