ON THE SPECTRAL CHARACTERISTICS OF SIGNLESS LAPLACIAN MATRIX

In this paper, we present a comprehensive study on the spectral properties of the signless Laplacian matrix of the maximal graph. Specifically, we characterize the spectral radius of the signless Laplacian matrix of the maximal graph $M(\Gamma(\mathbb{Z}_n))$. Moreover, we study the smallest signless Laplacian eigenvalue of the maximal graph and introduce an interaction with the algebraic connectivity of $M(\Gamma(\mathbb{Z}_n))$ for some definite values of $n$. Finally, we derive an explicit formula for the Wiener index in terms of signless Laplacian eigenvalues of the graph.