فهرست نشریات علمی دسترسی آزاد ایران

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 $\Gamma(U)$.