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For a commutative ring R with identity 1 6= 0, let the set Z(R) denote the set of zero-divisors and let Z-(R) = Z(R) n f0g be the set of non-zero zero divisors of R. The zero divisor graph of R, denoted by -(R), is a simple graph whose vertex set is Z-(R) and two vertices u; v 2 Z-(R) are adjacent if and only if uv = vu = 0. In this article, we and the signless Laplacian spectrum of the zero divisor graphs -(Zn) for n = pM1 qM2, where p < q are primes and M1;M2 are positive integers. [ABSTRACT FROM AUTHOR]

For a finite group G, the power graph P(G) is a connected simple graph, whose vertex set is the set of elements of G and two vertices are connected by an edge if and only if one is the power of the other. In this article, we obtain sharp bounds for the distance signless Laplacian spectral radius of the power graphs of cyclic groups, dihedral and dicyclic groups. Furthermore, we characterize the extremal power graphs attaining such bounds and give some open problems. [ABSTRACT FROM AUTHOR]

For a commutative ring R with identity 1 6= 0, let the set Z(R) denote the set of zero-divisors and let Z-(R) = Z(R) n f0g be the set of non-zero zero divisors of R. The zero divisor graph of R, denoted by -(R), is a simple graph whose vertex set is Z-(R) and two vertices u; v 2 Z-(R) are adjacent if and only if uv = vu = 0. In this article, we and the signless Laplacian spectrum of the zero divisor graphs -(Zn) for n = pM1 qM2, where p < q are primes and M1;M2 are positive integers. [ABSTRACT FROM AUTHOR]