International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3711 2020 2020 Department of Mathematics, Irbid National University, Irbid, Jordan Eman Eman Department of Mathematics, Yarmouk University, Irbid, Jordan Edris Rawashdeh Department of Basic Scientific Sciences, Al-Huson University College, Al-Balqa Applied University, Irbid, Jordan Eman Rawshdeh 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. 2025 2025 241 250 10.54216/IJNS.260218 https://www.americaspg.com/articleinfo/21/show/3711