Note on the Sum of Powers of Normalized Signless Laplacian Eigenvalues of Graphs

Document Type: Original Scientific Paper

Author

Konya, Turkey

10.22052/mir.2019.208991.1180

Abstract

In this paper, for a connected graph G and a real alpha (not equal to) 0, we define a new graph invariant sigma_alpha (G)-as the sum of the alphath powers of the normalized signless Laplacian eigenvalues of G. Note that sigma_1/2 (G) is equal to Randic (normalized) incidence energy which have been recently studied in the literature [5, 15]. We present some bounds on sigma_alpha(G) (alpha (not equal to) 0, 1) and also consider the special case alpha = 1/2.

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