ON NORMALIZED SIGNLESS LAPLACIAN RESOLVENT ENERGY

Let G be a simple connected graph with n vertices. Denote by (Formula presented) the normalized signless Laplacian matrix of graph G, where Q (G) and D (G) are the signless Laplacian and diagonal degree matrices of G, respectively. The eigenvalues of matrix (Formula presented), are normalized signless Laplacian eigenvalues of G. In this paper, we introduce the normalized signless Laplacian resolvent energy of G as (Formula presented). We also obtain some lower and upper bounds for ERNS (G) as well as its relationships with other energies and signless Kemeny’s constant.