Abstract
The A(gamma) matrix of a graph G is determined by A(gamma)(G) = (1 - gamma) A(G) + gamma D(G), where 0 <= gamma <= 1, A (G) and D(G) are the adjacency and the diagonal matrices of node degrees, respectively. In this case, the A(gamma) matrix brings together the spectral theories of the adjacency, the Laplacian, and the signless Laplacian matrices, and many more gamma adjacency-type matrices. In this paper, we obtain the A(gamma) eigenvalues of zero divisor graphs of the integer modulo rings and the von Neumann rings. These results generalize the earlier published spectral theories of the adjacency, the Laplacian and the signless Laplacian matrices of zero divisor graphs.