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

• Autorzy: Li Su , Hong-Hai Li , Jing Zhang
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

clique number; kite graph; signless Laplacian; spectral radius

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2014
• Tom: 34
• Numer: 1
• Strony: 95-102

Daty

wydano

2014-02-01

online

2014-02-14

Twórcy

autor

Li Su

• College of Mathematics and Information Science Jiangxi Normal University Nanchang, 330022, P.R. China

autor

Hong-Hai Li

• College of Mathematics and Information Science Jiangxi Normal University Nanchang, 330022, P.R. China

autor

Jing Zhang

• College of Mathematics and Information Science Jiangxi Normal University Nanchang, 330022, P.R. China

Bibliografia

• [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]
• [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]
• [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.
• [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]
• [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]
• [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]
• [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]
• [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.

Identyfikatory

DOI

10.7151/dmgt.1718