A characterization of strongly regular graphs in terms of the largest signless Laplacian eigenvalues

Feng Lei Fan; Chih-wen Weng

doi:10.1016/j.laa.2016.05.009

A characterization of strongly regular graphs in terms of the largest signless Laplacian eigenvalues

Feng Lei Fan^*, Chih-wen Weng

^*Corresponding author for this work

Department of Applied Mathematics

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

3 Scopus citations

Abstract

Let G be a simple graph of order n with maximum degree Δ. Let λ (resp. μ) denote the maximum number of common neighbors of a pair of adjacent vertices (resp. nonadjacent distinct vertices) of G. Let q(G) denote the largest eigenvalue of the signless Laplacian matrix of G. We show thatq(G)≤Δ-μ4+^(Δ-μ4)2+(1+λ)Δ+μ(n-1)-^Δ2, with equality if and only if G is a strongly regular graph with parameters (n,Δ,λ,μ).

Original language	English
Pages (from-to)	1-5
Number of pages	5
Journal	Linear Algebra and Its Applications
Volume	506
DOIs	https://doi.org/10.1016/j.laa.2016.05.009
State	Published - 1 Oct 2016

Keywords

Signless Laplacian matrix
Strongly regular graphs

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10.1016/j.laa.2016.05.009

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title = "A characterization of strongly regular graphs in terms of the largest signless Laplacian eigenvalues",

abstract = "Let G be a simple graph of order n with maximum degree Δ. Let λ (resp. μ) denote the maximum number of common neighbors of a pair of adjacent vertices (resp. nonadjacent distinct vertices) of G. Let q(G) denote the largest eigenvalue of the signless Laplacian matrix of G. We show thatq(G)≤Δ-μ4+(Δ-μ4)2+(1+λ)Δ+μ(n-1)-Δ2, with equality if and only if G is a strongly regular graph with parameters (n,Δ,λ,μ).",

keywords = "Signless Laplacian matrix, Strongly regular graphs",

author = "Fan, {Feng Lei} and Chih-wen Weng",

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AU - Weng, Chih-wen

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N2 - Let G be a simple graph of order n with maximum degree Δ. Let λ (resp. μ) denote the maximum number of common neighbors of a pair of adjacent vertices (resp. nonadjacent distinct vertices) of G. Let q(G) denote the largest eigenvalue of the signless Laplacian matrix of G. We show thatq(G)≤Δ-μ4+(Δ-μ4)2+(1+λ)Δ+μ(n-1)-Δ2, with equality if and only if G is a strongly regular graph with parameters (n,Δ,λ,μ).

AB - Let G be a simple graph of order n with maximum degree Δ. Let λ (resp. μ) denote the maximum number of common neighbors of a pair of adjacent vertices (resp. nonadjacent distinct vertices) of G. Let q(G) denote the largest eigenvalue of the signless Laplacian matrix of G. We show thatq(G)≤Δ-μ4+(Δ-μ4)2+(1+λ)Δ+μ(n-1)-Δ2, with equality if and only if G is a strongly regular graph with parameters (n,Δ,λ,μ).

KW - Signless Laplacian matrix

KW - Strongly regular graphs

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DO - 10.1016/j.laa.2016.05.009

M3 - Article

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SP - 1

EP - 5

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

A characterization of strongly regular graphs in terms of the largest signless Laplacian eigenvalues

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