Laplacian eigenvalues of the extended zero divisor graph of some finite commutative rings

Abstract

In this paper, we have evaluated the Laplacian eigenvalues of the extended zero divisor graph for certain finite commutative rings. Additionally, we present the conditions under which the Laplacian spectral radius of the extended zero divisor graph is equivalent to the order of the graph. Furthermore, we calculate the clique number, independent number, domination number, and connected domination number of the extended zero divisor graph for specific finite commutative rings.