On the diameter of INZD-graph

Kadem, Sameer; Aubad, Ali A.

doi:10.47974/JDMSC-2712

Open Access Research Article

On the diameter of INZD-graph

Sameer Kademsamir.kadhum2303@sc.uobaghdad.edu.iqDepartment of MathematicsCollege of ScienceUniversity of BaghdadBaghdad, IraqView full profile → , ^*Ali A. AubadCorresponding authorali.abd@sc.uobaghdad.edu.iqDepartment of MathematicsCollege of ScienceUniversity of BaghdadBaghdad, IraqView full profile →

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pp. 2109–2116Vol. 29Issue 5May 2026DOI: 10.47974/JDMSC-2712 Crossmark XML

Received:: 01 Jan 2026
Published Online:: 22 May 2026
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-2712
Pages:: 2109–2116

Abstract

Let R be a ring and let J be a proper ideal of R. In this work, we focus on the ideal-based non-zero divisor graph ∅J (R), whose vertices consist of the elements lying outside J, while adjacency is determined relative to this fixed ideal. main interest here is to understand how distances behave in this setting, especially when the graph is assumed to be connected. show that once ∅J(R) is connected and contains at least five vertices, the distance between any two vertices does not exceed two, apart from a few exceptional situations that are treated separately. In this way, the classical diameter bounds known for zero-divisor and non-zero divisor graphs naturally extend to the ideal-based context, while at the same time revealing how the presence of an ideal can subtly reshape the overall structure of the graph.

Keywords

ZD-graph Diameter Trees Connectivity

Subject Classifications

05C2505C1205C0505C40

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