Remarks on the sum of powers of normalized signless Laplacian eigenvalues of graphs

Author:

Bozkurt Altındağ1,Milovanovic Igor2,Milovanovic Emina2,Matejic Marjan2

Affiliation:

1. Faculty of Science, Selçuk University, Konya, Turkey

2. Faculty of Electronic Engineering, University of Niš, Niš, Serbia

Abstract

Let G = (V, E), V = {v1, v2,..., vn}, be a simple connected graph of order n and size m. Denote by ?+1 ? ?+2 ?...? ?+n ? 0 the normalized signless Laplacian eigenvalues of G, and by ??(G) the sum of ?-th powers of the normalized signless Laplacian eigenvalues of a connected graph. The paper deals with bounds of ??. Some special cases, when ? = 12 and ? = ?1, are also considered.

Publisher

National Library of Serbia

Reference30 articles.

1. M. Bianchi, A. Cornaro, J. L. Palacios, A. Torriero, Bounding the sum of powers of normalized Laplacian eigenvalues of graph through majorization method, MATCH Commun. Math. Comput. Chem. 70 (2013) 707-716.

2. Ş. B. Bozkurt, D. Bozkurt, On the sum of powers of normalized Laplacian eigenvalues of graphs, MATCH Commun. Math. Comput. Chem. 68 (2012) 917-930.

3. Ş. B. Bozkurt Altındağ, Note on the sum of powers of normalized signless Laplacian eigenvalues of graphs, Math. Interdisc. Res. 4 (2) (2019) 171-182.

4. Ş. B. Bozkurt Altındağ, Sum of powers of normalized signless Laplacian eigenvalues and Randić (normalized) incidence energy of graphs, Bull. Inter. Math. Virtual Inst. 11 (1) (2021) 135-146.

5. Ş. B. Bozkurt, A. D. Gungor, I. Gutman, A. S. Cevik, Randić matrix and Randić energy, MATCH Commun. Math. Comput. Chem. 64 (2010), 239-250.

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