A sharp lower bound on the signless Laplacian index of graphs with (κ,τ)-regular sets-Reference-Cited by-同舟云学术

A sharp lower bound on the signless Laplacian index of graphs with (κ,τ)-regular sets

Published:2018-02-01 Issue:1 Volume:6 Page:68-76
ISSN:2300-7451
Container-title:Special Matrices
language:en
Short-container-title:

Author:

Andeelić Milica¹,Cardoso Domingos M.²,Pereira António²

Affiliation:

1. Department of Mathematics, Kuwait University, Safat 13060, Kuwait, and Departamento de Matemática, Universidade de Aveiro, 3810-193 Aveiro , Portugal

2. Departamento de Matemática, Universidade de Aveiro, 3810-193 Aveiro , Portugal

Abstract

Abstract A new lower bound on the largest eigenvalue of the signless Laplacian spectra for graphs with at least one (κ,τ)regular set is introduced and applied to the recognition of non-Hamiltonian graphs or graphs without a perfect matching. Furthermore, computational experiments revealed that the introduced lower bound is better than the known ones. The paper also gives sufficient condition for a graph to be non Hamiltonian (or without a perfect matching).

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology,Algebra and Number Theory

Link

https://www.degruyter.com/document/doi/10.1515/spma-2018-0007/pdf

Reference9 articles.

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2. [2] D.M. Cardoso, D. Cvetkovic, Graphs with least eigenvalue −2 attaining a convex quadratic upper bound for the stability number, Bull. Acad. Serbe Sci. Arts, CI. Sci. Math. Natur. Sci. Math., 3 (2006), 41-55.

3. [3] D. Cvetkovic, P. Rowlinson, S. Simic, Eigenvalue bounds for the signless Laplacian, Publ. Inst. Math. (deograd) (N.S.) 81(95) (2007), 11-27.

4. [4] D. Cvetkovic, P. Rowlinson, S. Simic, Signless Laplacian of finite graphs, Linear Algebra Appl. 423 (2007), 155-171.

5. [5] D. Cvetkovic, P. Rowlinson, S. Simic, An Introduction to the Theory of Graph Spectra, Cambridge University Press, 2010.

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