Abstract
Abstract Let 𝑅 be a commutative ring with identity 1 ≠ 0 1\neq 0 and let Z ( R ) ′ Z(R)^{\prime} be the set of all non-zero and non-unit elements of ring 𝑅. Further, Γ ′ ( R ) \Gamma^{\prime}(R) denotes the cozero-divisor graph of 𝑅, is an undirected graph with vertex set Z ( R ) ′ Z(R)^{\prime} , and w ∉ z R w\notin zR and z ∉ w R z\notin wR if and only if two distinct vertices 𝑤 and 𝑧 are adjacent, where q R qR is the ideal generated by the element 𝑞 in 𝑅. In this paper, we find the signless Laplacian eigenvalues of the graphs Γ ′ ( Z n ) \Gamma^{\prime}(\mathbb{Z}_{n}) for n = p 1 N p 2 p 3 n=p_{1}^{N}p_{2}p_{3} and p 1 N p 2 M p 3 p_{1}^{N}p_{2}^{M}p_{3} , where p 1 , p 2 , p 3 p_{1},p_{2},p_{3} are distinct primes and N , M N,M are positive integers. We also show that the cozero-divisor graph Γ ′ ( Z p 1 p 2 ) \Gamma^{\prime}(\mathbb{Z}_{p_{1}p_{2}}) is a signless Laplacian integral.
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