Browsing by Author "Khoramdel, Mehdi"

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    A graph associated to a commutative semiring
    (Ankara Üniversitesi, 2021) Khoramdel, Mehdi; Other; Other
    Let R be a commutative finite semiring with nonzero identity and H be an arbitrary multiplicatively closed subset R. The generalized identity-summand graph of R is the (simple) graph GH(R) with all elements of R as the vertices, and two distinct vertices x and y are adjacent if and only if x+y∈H. In this paper, we study some basic properties of GH(R). Moreover, we characterize the planarity, chromatic number, clique number and independence number of GH(R).
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    On a graph of ideals of a commutative ring
    (Ankara Üniversitesi Fen Fakültesi, 2019-08-01) Khoramdel, Mehdi; Atani, Shahabaddin Ebrahimi; Pishhesari, Saboura Dolati; Other; Other
    In this paper, we introduce and investigate a new graph of a commutative ring R, denoted by G(R), with all nontrivial ideals of R as vertices, and two distinct vertices I and J are adjacent if and only if ann(I∩J)=ann(I)+ann(J). In this article, the basic properties and possible structures of the graph G(R) are studied and investigated as diameter, girth, clique number, cut vertex and domination number. We characterize all rings R for which G(R) is planar, complete and complete r-partite. We show that, if (R,M) is a local Artinian ring, then G(R) is complete if and only if Soc(R) is simple. Also, it is shown that if R is a ring with G(R) is r-regular, then either G(R) is complete or null graph. Moreover, we show that if R is an Artinian ring, then R is a serial ring if and only if G(R/I) is complete for each ideal I of R.