A generalized ideal based-zero divisor graphs of near-rings
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In this paper, we introduce the generalized ideal-based zero-divisor graph structure of near-ring N, denoted by Γ_{I}(N). It is shown that if I is a completely reflexive ideal of N, then every two vertices in Γ_{I}(N) are connected by a path of length at most 3, and if Γ_{I}(N) contains a cycle, then the core K of Γ_{I}(N) is a union of triangles and rectangles. We have shown that if Γ_{I}(N) is a bipartite graph for a completely semiprime ideal I of N, then N has two prime ideals whose intersection is I.
Abstract
In this paper, we introduce the generalized ideal-based zero-divisor graph structure of near-ring N, denoted by Γ_{I}(N). It is shown that if I is a completely reflexive ideal of N, then every two vertices in Γ_{I}(N) are connected by a path of length at most 3, and if Γ_{I}(N) contains a cycle, then the core K of Γ_{I}(N) is a union of triangles and rectangles. We have shown that if Γ_{I}(N) is a bipartite graph for a completely semiprime ideal I of N, then N has two prime ideals whose intersection is I.
참고문헌 (11)
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