The algebraic connectivity of lollipop graphs

Ji Ming Guo; Wai Chee Shiu; Jianxi Li

doi:10.1016/j.laa.2010.12.020

The algebraic connectivity of lollipop graphs

Ji Ming Guo
, Wai Chee Shiu
, Jianxi Li

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

11 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	2204-2210
Number of pages	7
Journal	Linear Algebra and Its Applications
Volume	434
Issue number	10
DOIs	https://doi.org/10.1016/j.laa.2010.12.020
Publication status	Published - 15 May 2011

User-Defined Keywords

Algebraic connectivity
Characteristic polynomial
Lollipop graph

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10.1016/j.laa.2010.12.020

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title = "The algebraic connectivity of lollipop graphs",

abstract = "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.",

keywords = "Algebraic connectivity, Characteristic polynomial, Lollipop graph",

author = "Guo, \{Ji Ming\} and Shiu, \{Wai Chee\} and Jianxi Li",

note = "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).",

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doi = "10.1016/j.laa.2010.12.020",

language = "English",

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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 - https://www.scopus.com/pages/publications/79951681657

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 -

The algebraic connectivity of lollipop graphs

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