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International Journal of Neutrosophic Science

Volume 26 , Issue 2 , PP: 241-250, 2025 | Cite this article as | XML | Html | PDF | Full Length Article

Clean Graphs over Rings of Order P^2

Heba Adel Abdelkarim 1 , Edris Rawashdeh 2 , Eman Rawshdeh 3 *

  • 1 Department of Mathematics, Irbid National University, Irbid, Jordan - (dr.heba@inu.edu.jo)
  • 2 Department of Mathematics, Yarmouk University, Irbid, Jordan - (edris@yu.edu.jo)
  • 3 Department of Basic Scientific Sciences, Al-Huson University College, Al-Balqa Applied University, Irbid, Jordan - (eman.rw@bau.edu.jo)

    • Doi: https://doi.org/10.54216/IJNS.260218

    Received: January 10, 2025 Revised: March 02, 2025 Accepted: March 13, 2025
    Abstract

    Assume R is a commutative ring with unity. The clean graph CL(R) is defined in which every vertex has the form (a, v), where a is an idempotent in R and v is a unit. In CL(R), two distinct vertices (a1, v1) and (a2, v2) are adjacent if a1a2 = a2a1 = 0 or v1v2 = v2v1 = 1. In this paper, we show that the clean graph CL(R) over a ring of order p2 can be defined only if R is one of the rings: Zp2 ,Zp ⊕Zp,Zp(+)Zp and GF(p2). Then, we study the spectrum, the biclique partition number, and the eigensharp property for the these clean graphs.

    Keywords :

    Commutative Ring , Clean Graph , Spectrum of graph , Biclique partition number , Eigensharp graph

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    Cite This Article As :
    Adel, Heba. , Rawashdeh, Edris. , Rawshdeh, Eman. Clean Graphs over Rings of Order P^2. International Journal of Neutrosophic Science, vol. , no. , 2025, pp. 241-250. DOI: https://doi.org/10.54216/IJNS.260218
    Adel, H. Rawashdeh, E. Rawshdeh, E. (2025). Clean Graphs over Rings of Order P^2. International Journal of Neutrosophic Science, (), 241-250. DOI: https://doi.org/10.54216/IJNS.260218
    Adel, Heba. Rawashdeh, Edris. Rawshdeh, Eman. Clean Graphs over Rings of Order P^2. International Journal of Neutrosophic Science , no. (2025): 241-250. DOI: https://doi.org/10.54216/IJNS.260218
    Adel, H. , Rawashdeh, E. , Rawshdeh, E. (2025) . Clean Graphs over Rings of Order P^2. International Journal of Neutrosophic Science , () , 241-250 . DOI: https://doi.org/10.54216/IJNS.260218
    Adel H. , Rawashdeh E. , Rawshdeh E. [2025]. Clean Graphs over Rings of Order P^2. International Journal of Neutrosophic Science. (): 241-250. DOI: https://doi.org/10.54216/IJNS.260218
    Adel, H. Rawashdeh, E. Rawshdeh, E. "Clean Graphs over Rings of Order P^2," International Journal of Neutrosophic Science, vol. , no. , pp. 241-250, 2025. DOI: https://doi.org/10.54216/IJNS.260218

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