# The Minimum Spectral Radius of Signless Laplacian of Graphs with a Given Clique Number

Li Su; Hong-Hai Li; Jing Zhang

Discussiones Mathematicae Graph Theory (2014)

- Volume: 34, Issue: 1, page 95-102
- ISSN: 2083-5892

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topLi Su, Hong-Hai Li, and Jing Zhang. "The Minimum Spectral Radius of Signless Laplacian of Graphs with a Given Clique Number." Discussiones Mathematicae Graph Theory 34.1 (2014): 95-102. <http://eudml.org/doc/268308>.

@article{LiSu2014,

abstract = {In this paper we observe that the minimal signless Laplacian spectral radius is obtained uniquely at the kite graph PKn−ω,ω among all connected graphs with n vertices and clique number ω. In addition, we show that the spectral radius μ of PKm,ω (m ≥ 1) satisfies [...] More precisely, for m > 1, μ satisfies the equation [...] where [...] and [...] . At last the spectral radius μ(PK∞,ω) of the infinite graph PK∞,ω is also discussed.},

author = {Li Su, Hong-Hai Li, Jing Zhang},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {clique number; kite graph; signless Laplacian; spectral radius},

language = {eng},

number = {1},

pages = {95-102},

title = {The Minimum Spectral Radius of Signless Laplacian of Graphs with a Given Clique Number},

url = {http://eudml.org/doc/268308},

volume = {34},

year = {2014},

}

TY - JOUR

AU - Li Su

AU - Hong-Hai Li

AU - Jing Zhang

TI - The Minimum Spectral Radius of Signless Laplacian of Graphs with a Given Clique Number

JO - Discussiones Mathematicae Graph Theory

PY - 2014

VL - 34

IS - 1

SP - 95

EP - 102

AB - In this paper we observe that the minimal signless Laplacian spectral radius is obtained uniquely at the kite graph PKn−ω,ω among all connected graphs with n vertices and clique number ω. In addition, we show that the spectral radius μ of PKm,ω (m ≥ 1) satisfies [...] More precisely, for m > 1, μ satisfies the equation [...] where [...] and [...] . At last the spectral radius μ(PK∞,ω) of the infinite graph PK∞,ω is also discussed.

LA - eng

KW - clique number; kite graph; signless Laplacian; spectral radius

UR - http://eudml.org/doc/268308

ER -

## References

top- [1] Y. Chen, Properties of spectra of graphs and line graphs, Appl. Math. J. Chinese Univ. (B) 17 (2002) 371-376. doi:10.1007/s11766-002-0017-7[Crossref] Zbl1022.05046
- [2] D. Cvetković, P. Rowlinson and S.K. Simić, Signless Laplacians of finite graphs, Linear Algebra Appl. 423 (2007) 155-171. doi:10.1016/j.laa.2007.01.009[WoS][Crossref] Zbl1113.05061
- [3] D. Cvetković and S.K. Simić, Towards a spectral theory of graphs based on signless Laplacian I, Publ. Inst. Math. (Beograd) 99 (2009) 19-33. Zbl1224.05293
- [4] D. Cvetković and S.K. Simić, Towards a spectral theory of graphs based on signless Laplacian II, Linear Algebra Appl. 432 (2010) 2257-2272. doi:10.1016/j.laa.2009.05.020[Crossref] Zbl1218.05089
- [5] E.R. van Dam and W. Haemers, Which graphs are determined by their spectrum?, Linear Algebra Appl. 373 (2003) 241-272. doi:10.1016/S0024-3795(03)00483-X[Crossref] Zbl1026.05079
- [6] W. Haemers and E. Spence, Enumeration of cospectral graphs, European J. Combin. 25 (2004) 199-211. doi:10.1016/S0195-6698(03)00100-8[Crossref] Zbl1033.05070
- [7] B. Mohar and W. Woess, A survey on spectra of infnite graphs, Bull. London Math. Soc. 21 (1989) 209-234. doi:10.1112/blms/21.3.209[Crossref] Zbl0645.05048
- [8] B. Mohar, On the Laplacian coefficients of acyclic graphs, Linear Algebra Appl. 722 (2007) 736-741. doi:10.1016/j.laa.2006.12.005[Crossref][WoS]
- [9] D. Stevanović and P. Hansen, The minimum spectral radius of graphs with a given clique number , Electron. J. Linear Algebra 17 (2008) 110-117. Zbl1148.05306

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