Some graphs determined by their (signless) Laplacian spectra

Muhuo Liu; Haiying Shan; Kinkar Ch Das

doi:10.1016/j.laa.2014.02.027

Some graphs determined by their (signless) Laplacian spectra

Muhuo Liu
, Haiying Shan
, Kinkar Ch Das

Department of Mathematics

Nanjing Normal University
South China Agricultural University
Tongji University

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

14 Scopus citations

Abstract

A graph G is L-DS (respectively, Q-DS) if there is no other non-isomorphic graph with the same (respectively, signless) Laplacian spectrum as G. Let ^G1â̂̈^G2 be the join graph of graphs ^G1 and ^G2, and Ur,_n-r the graph obtained by attaching n-r pendent vertices to a vertex of ^Cr (the cycle of order r). In this paper, we prove that if G is L-DS and the algebraic connectivity of G is less than three, then ^Ktâ̂̈G is L-DS under certain condition, which extends the main result of Zhou and Bu (2012) [24]. Also, Ur,_n-r is proved to be Q-DS for r≥3.

Original language	English
Pages (from-to)	154-165
Number of pages	12
Journal	Linear Algebra and Its Applications
Volume	449
DOIs	https://doi.org/10.1016/j.laa.2014.02.027
State	Published - 15 May 2014

Keywords

Algebraic connectivity
Join graph
Laplacian spectrum
Signless Laplacian spectrum

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10.1016/j.laa.2014.02.027

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title = "Some graphs determined by their (signless) Laplacian spectra",

abstract = "A graph G is L-DS (respectively, Q-DS) if there is no other non-isomorphic graph with the same (respectively, signless) Laplacian spectrum as G. Let G1{\^a}{\"̂}G2 be the join graph of graphs G1 and G2, and Ur,n-r the graph obtained by attaching n-r pendent vertices to a vertex of Cr (the cycle of order r). In this paper, we prove that if G is L-DS and the algebraic connectivity of G is less than three, then Kt{\^a}{\"̂}G is L-DS under certain condition, which extends the main result of Zhou and Bu (2012) [24]. Also, Ur,n-r is proved to be Q-DS for r≥3.",

keywords = "Algebraic connectivity, Join graph, Laplacian spectrum, Signless Laplacian spectrum",

author = "Muhuo Liu and Haiying Shan and Das, \{Kinkar Ch\}",

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doi = "10.1016/j.laa.2014.02.027",

language = "English",

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journal = "Linear Algebra and Its Applications",

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T1 - Some graphs determined by their (signless) Laplacian spectra

AU - Liu, Muhuo

AU - Shan, Haiying

AU - Das, Kinkar Ch

PY - 2014/5/15

Y1 - 2014/5/15

N2 - A graph G is L-DS (respectively, Q-DS) if there is no other non-isomorphic graph with the same (respectively, signless) Laplacian spectrum as G. Let G1â̂̈G2 be the join graph of graphs G1 and G2, and Ur,n-r the graph obtained by attaching n-r pendent vertices to a vertex of Cr (the cycle of order r). In this paper, we prove that if G is L-DS and the algebraic connectivity of G is less than three, then Ktâ̂̈G is L-DS under certain condition, which extends the main result of Zhou and Bu (2012) [24]. Also, Ur,n-r is proved to be Q-DS for r≥3.

AB - A graph G is L-DS (respectively, Q-DS) if there is no other non-isomorphic graph with the same (respectively, signless) Laplacian spectrum as G. Let G1â̂̈G2 be the join graph of graphs G1 and G2, and Ur,n-r the graph obtained by attaching n-r pendent vertices to a vertex of Cr (the cycle of order r). In this paper, we prove that if G is L-DS and the algebraic connectivity of G is less than three, then Ktâ̂̈G is L-DS under certain condition, which extends the main result of Zhou and Bu (2012) [24]. Also, Ur,n-r is proved to be Q-DS for r≥3.

KW - Algebraic connectivity

KW - Join graph

KW - Laplacian spectrum

KW - Signless Laplacian spectrum

UR - https://www.scopus.com/pages/publications/84896760029

U2 - 10.1016/j.laa.2014.02.027

DO - 10.1016/j.laa.2014.02.027

M3 - Article

AN - SCOPUS:84896760029

SN - 0024-3795

VL - 449

SP - 154

EP - 165

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Some graphs determined by their (signless) Laplacian spectra

Abstract

Keywords

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