New upper and lower bound for the signless  Laplacian spectral radius

doi:10.3969/j.issn.0253-2778.2015.12.002

Journal of University of Science and Technology of China ›› 2015, Vol. 45 ›› Issue (12): 972-975.DOI: 10.3969/j.issn.0253-2778.2015.12.002

• Research Articles:Mathematics • Previous Articles Next Articles

New upper and lower bound for the signless Laplacian spectral radius

ZHAO Hongting, ZHANG Hailiang

1.School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China; 2.Department of Mathematics, Taizhou University, Linhai 317000, China

Received:2014-11-03 Revised:2015-06-01 Accepted:2015-06-01 Online:2023-03-27 Published:2015-06-01
Contact: ZHAO Hongting
About author:ZHAO Hongting (corresponding author), male born in 1979, master/lecturer. Research field: combinatorial analysis.
Supported by:
Supported by the National Science Foundation of Zhejiang (Y6110054).

Abstract

Abstract: Let D be the degree diagonal matrix of G, A be the adjacency matrix of G, Q=D+A be the signless Laplacian matrix of G. Let ξ(G) be the signless Laplacian spectral radius of G. Here the degree of graph was extended to k-degree, and average degree to k-average degree of a graph. A new upper and a new lower bound for the signless spectral radius of a graph G was obtained. Comparisons were made of the result with several classical results on the ξ(G).

Key words: graph, Laplacian spectral radius, signless Laplacian spectral radius, k-degree, average k-degree

CLC Number:

O157.1

ZHAO Hongting, ZHANG Hailiang. New upper and lower bound for the signless Laplacian spectral radius[J]. Journal of University of Science and Technology of China, 2015, 45(12): 972-975.

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New upper and lower bound for the signless Laplacian spectral radius

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