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: [email protected] (J.-M. Guo), [email protected] (W.C. Shiu), [email protected] (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 - Journal 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 -