TY - JOUR

T1 - The algebraic connectivity of lollipop graphs

AU - Guo, Ji Ming

AU - SHIU, Wai Chee

AU - Li, Jianxi

N1 - Funding Information:
Supported by the National Science Foundation of China (No. 10871204); the Fundamental Research Funds for the Central Un∗Correspondingauthor.iversities(No. 09CX04003A); FRG, Hong Kong Baptist University. E-mail addresses: jimingguo@hotmail.com (J.-M. Guo), wcshiu@hkbu.edu.hk (W.C. Shiu), fzjxli@tom.com (J. Li).

PY - 2011/5/15

Y1 - 2011/5/15

N2 - Let Cn,g be the lollipop graph obtained by appending a g-cycle Cg to a pendant vertex of a path on n-g vertices. In 2002, Fallat, Kirkland and Pati proved that for n≥3g-12 and g≥4, α(Cn,g)>α(Cn,g-1). In this paper, we prove that for g≥4, α(Cn,g)>α(Cn,g-1) for all n, where α(Cn,g) is the algebraic connectivity of Cn,g.

AB - Let Cn,g be the lollipop graph obtained by appending a g-cycle Cg to a pendant vertex of a path on n-g vertices. In 2002, Fallat, Kirkland and Pati proved that for n≥3g-12 and g≥4, α(Cn,g)>α(Cn,g-1). In this paper, we prove that for g≥4, α(Cn,g)>α(Cn,g-1) for all n, where α(Cn,g) is the algebraic connectivity of Cn,g.

KW - Algebraic connectivity

KW - Characteristic polynomial

KW - Lollipop graph

UR - http://www.scopus.com/inward/record.url?scp=79951681657&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2010.12.020

DO - 10.1016/j.laa.2010.12.020

M3 - Article

AN - SCOPUS:79951681657

SN - 0024-3795

VL - 434

SP - 2204

EP - 2210

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 10

ER -