Proof of conjectures involving the largest and the smallest signless Laplacian eigenvalues of graphs

Kinkar Ch Das

doi:10.1016/j.disc.2011.10.030

Proof of conjectures involving the largest and the smallest signless Laplacian eigenvalues of graphs

Kinkar Ch Das

Department of Mathematics

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

20 Scopus citations

Abstract

Let G=(V,E) be a simple graph. Denote by D(G) the diagonal matrix of its vertex degrees and by A(G) its adjacency matrix. Then the signless Laplacian matrix of G is Q(G)=D(G)+A(G). In [5], Cvetkovi et al. (2007) have given conjectures on signless Laplacian eigenvalues of G (see also Aouchiche and Hansen (2010) [1], Oliveira et al. (2010) [14]). Here we prove two conjectures.

Original language	English
Pages (from-to)	992-998
Number of pages	7
Journal	Discrete Mathematics
Volume	312
Issue number	5
DOIs	https://doi.org/10.1016/j.disc.2011.10.030
State	Published - 6 Mar 2012

Keywords

Graph
Signless Laplacian matrix
The largest signless Laplacian eigenvalue
The smallest signless Laplacian eigenvalue

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10.1016/j.disc.2011.10.030

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abstract = "Let G=(V,E) be a simple graph. Denote by D(G) the diagonal matrix of its vertex degrees and by A(G) its adjacency matrix. Then the signless Laplacian matrix of G is Q(G)=D(G)+A(G). In [5], Cvetkovi et al. (2007) have given conjectures on signless Laplacian eigenvalues of G (see also Aouchiche and Hansen (2010) [1], Oliveira et al. (2010) [14]). Here we prove two conjectures.",

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AB - Let G=(V,E) be a simple graph. Denote by D(G) the diagonal matrix of its vertex degrees and by A(G) its adjacency matrix. Then the signless Laplacian matrix of G is Q(G)=D(G)+A(G). In [5], Cvetkovi et al. (2007) have given conjectures on signless Laplacian eigenvalues of G (see also Aouchiche and Hansen (2010) [1], Oliveira et al. (2010) [14]). Here we prove two conjectures.

KW - Graph

KW - Signless Laplacian matrix

KW - The largest signless Laplacian eigenvalue

KW - The smallest signless Laplacian eigenvalue

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JF - Discrete Mathematics

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ER -

Proof of conjectures involving the largest and the smallest signless Laplacian eigenvalues of graphs

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Keywords

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