On the extremal values of the second largest q-eigenvalue

Mustapha Aouchiche; Pierre Hansen; Claire Lucas

doi:10.1016/j.laa.2011.03.051

On the extremal values of the second largest q-eigenvalue

Mustapha Aouchiche, Pierre Hansen, Claire Lucas

Research output: Contribution to journal › Article › peer-review

19 Citations (Scopus)

Abstract

We study extremal graphs for the extremal values of the second largest Q-eigenvalue of a connected graph. We first characterize all simple connected graphs with second largest signless Laplacian eigenvalue at most 3. The second part of the present paper is devoted to the study of the graphs that maximize the second largest Q-eigenvalue. We construct families of such graphs and prove that some of theses families are minimal for the fact that they maximize the second largest signless Laplacian eigenvalue.

Original language	English
Pages (from-to)	2591-2606
Number of pages	16
Journal	Linear Algebra and Its Applications
Volume	435
Issue number	10
DOIs	https://doi.org/10.1016/j.laa.2011.03.051
Publication status	Published - Nov 15 2011
Externally published	Yes

Keywords

Critical graph
Extremal graph
Second largest eigenvalue
Signless Laplacian

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/j.laa.2011.03.051

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AU - Hansen, Pierre

AU - Lucas, Claire

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AB - We study extremal graphs for the extremal values of the second largest Q-eigenvalue of a connected graph. We first characterize all simple connected graphs with second largest signless Laplacian eigenvalue at most 3. The second part of the present paper is devoted to the study of the graphs that maximize the second largest Q-eigenvalue. We construct families of such graphs and prove that some of theses families are minimal for the fact that they maximize the second largest signless Laplacian eigenvalue.

KW - Critical graph

KW - Extremal graph

KW - Second largest eigenvalue

KW - Signless Laplacian

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On the extremal values of the second largest q-eigenvalue

Abstract

Keywords

ASJC Scopus subject areas

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