The smallest values of algebraic connectivity for unicyclic graphs

Jianxi Li; Ji Ming Guo; Wai Chee Shiu

doi:10.1016/j.dam.2010.05.009

The smallest values of algebraic connectivity for unicyclic graphs

Jianxi Li, Ji Ming Guo, Wai Chee Shiu

Department of Mathematics

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

12 Citations (Scopus)

Abstract

The algebraic connectivity of G is the second smallest eigenvalue of its Laplacian matrix. Let u_n be the set of all unicyclic graphs of order n. In this paper, we will provide the ordering of unicyclic graphs in u _n up to the last seven graphs according to their algebraic connectivities when n≥13. This extends the results of Liu and Liu [Y. Liu, Y. Liu, The ordering of unicyclic graphs with the smallest algebraic connectivity, Discrete Math. 309 (2009) 4315-4325] and Guo [J.-M. Guo, A conjecture on the algebraic connectivity of connected graphs with fixed girth, Discrete Math. 308 (2008) 5702-5711].

Original language	English
Pages (from-to)	1633-1643
Number of pages	11
Journal	Discrete Applied Mathematics
Volume	158
Issue number	15
DOIs	https://doi.org/10.1016/j.dam.2010.05.009
Publication status	Published - 6 Aug 2010

User-Defined Keywords

Algebraic connectivity
Order
Unicyclic graph

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10.1016/j.dam.2010.05.009

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title = "The smallest values of algebraic connectivity for unicyclic graphs",

abstract = "The algebraic connectivity of G is the second smallest eigenvalue of its Laplacian matrix. Let un be the set of all unicyclic graphs of order n. In this paper, we will provide the ordering of unicyclic graphs in u n up to the last seven graphs according to their algebraic connectivities when n≥13. This extends the results of Liu and Liu [Y. Liu, Y. Liu, The ordering of unicyclic graphs with the smallest algebraic connectivity, Discrete Math. 309 (2009) 4315-4325] and Guo [J.-M. Guo, A conjecture on the algebraic connectivity of connected graphs with fixed girth, Discrete Math. 308 (2008) 5702-5711].",

keywords = "Algebraic connectivity, Order, Unicyclic graph",

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

note = "Funding Information: Partially supported by FRG, Hong Kong Baptist University (No. FRG2/08-09/63 ); the National Science Foundation of China (No. 10871204 ) and the Fundamental Research Funds for the Central Universities (No. 09CX04003A ). ",

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T1 - The smallest values of algebraic connectivity for unicyclic graphs

AU - Li, Jianxi

AU - Guo, Ji Ming

AU - Shiu, Wai Chee

N1 - Funding Information: Partially supported by FRG, Hong Kong Baptist University (No. FRG2/08-09/63 ); the National Science Foundation of China (No. 10871204 ) and the Fundamental Research Funds for the Central Universities (No. 09CX04003A ).

PY - 2010/8/6

Y1 - 2010/8/6

N2 - The algebraic connectivity of G is the second smallest eigenvalue of its Laplacian matrix. Let un be the set of all unicyclic graphs of order n. In this paper, we will provide the ordering of unicyclic graphs in u n up to the last seven graphs according to their algebraic connectivities when n≥13. This extends the results of Liu and Liu [Y. Liu, Y. Liu, The ordering of unicyclic graphs with the smallest algebraic connectivity, Discrete Math. 309 (2009) 4315-4325] and Guo [J.-M. Guo, A conjecture on the algebraic connectivity of connected graphs with fixed girth, Discrete Math. 308 (2008) 5702-5711].

AB - The algebraic connectivity of G is the second smallest eigenvalue of its Laplacian matrix. Let un be the set of all unicyclic graphs of order n. In this paper, we will provide the ordering of unicyclic graphs in u n up to the last seven graphs according to their algebraic connectivities when n≥13. This extends the results of Liu and Liu [Y. Liu, Y. Liu, The ordering of unicyclic graphs with the smallest algebraic connectivity, Discrete Math. 309 (2009) 4315-4325] and Guo [J.-M. Guo, A conjecture on the algebraic connectivity of connected graphs with fixed girth, Discrete Math. 308 (2008) 5702-5711].

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KW - Order

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DO - 10.1016/j.dam.2010.05.009

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JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

IS - 15

ER -

The smallest values of algebraic connectivity for unicyclic graphs

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