On Normalized Signless Laplacian Resolvent Energy
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Authors: S. B. BOZKURT ALTINDAG, I. MILOVANOVIć, E. MILOVANOVIć AND M. MATEJIć
DOI: 10.46793/KgJMat2405.673A
Abstract:
Let G be a simple connected graph with n vertices. Denote by ℒ+ = D −1∕2Q D −1∕2 the normalized signless Laplacian matrix of graph G, where Q and D are the signless Laplacian and diagonal degree matrices of G, respectively. The eigenvalues of matrix ℒ+(G), 2 = γ1+ ≥ γ2+ ≥≥ γn+ ≥ 0, are normalized signless Laplacian eigenvalues of G. In this paper, we introduce the normalized signless Laplacian resolvent energy of G as ERNS = ∑ i=1n. We also obtain some lower and upper bounds for ERNS as well as its relationships with other energies and signless Kemeny’s constant.
Keywords:
Normalized signless Laplacian eigenvalues, normalized signless Laplacian resolvent energy, bounds.
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