The smallest values of algebraic connectivity for trees

Jian Xi Li; Ji Ming Guo; Wai Chee SHIU

doi:10.1007/s10114-012-0350-6

The smallest values of algebraic connectivity for trees

Jian Xi Li, Ji Ming Guo, Wai Chee SHIU

Department of Mathematics

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

5 Citations (Scopus)

Abstract

The algebraic connectivity of a graph G is the second smallest eigenvalue of its Laplacian matrix. Let ℐ _n be the set of all trees of order n. In this paper, we will provide the ordering of trees in ℐ _n up to the last eight trees according to their smallest algebraic connectivities when n ≥ 13. This extends the result of Shao et al.

Original language	English
Pages (from-to)	2021-2032
Number of pages	12
Journal	Acta Mathematica Sinica, English Series
Volume	28
Issue number	10
DOIs	https://doi.org/10.1007/s10114-012-0350-6
Publication status	Published - Sept 2012

Scopus Subject Areas

Mathematics(all)
Applied Mathematics

User-Defined Keywords

algebraic connectivity
ordering
Tree

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10.1007/s10114-012-0350-6

Cite this

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abstract = "The algebraic connectivity of a graph G is the second smallest eigenvalue of its Laplacian matrix. Let ℐ n be the set of all trees of order n. In this paper, we will provide the ordering of trees in ℐ n up to the last eight trees according to their smallest algebraic connectivities when n ≥ 13. This extends the result of Shao et al.",

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note = "Funding Information: Received June 25, 2010, accepted May 5, 2011 Supported by FRG, Hong Kong Baptist University, National Science Foundation (NSF) of China (Grant Nos. 10871204, 11101358), NSF of Fujian (Grant Nos. 2011J05014, 2011J01026), Project of Fujian Education Department (Grant No. JA11165), Fundamental Research Funds for the Central Universities (Grant No. 09CX04003A), Research Fund of Zhangzhou Normal University (Grant No. SJ1004) 1) Corresponding author",

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N2 - The algebraic connectivity of a graph G is the second smallest eigenvalue of its Laplacian matrix. Let ℐ n be the set of all trees of order n. In this paper, we will provide the ordering of trees in ℐ n up to the last eight trees according to their smallest algebraic connectivities when n ≥ 13. This extends the result of Shao et al.

AB - The algebraic connectivity of a graph G is the second smallest eigenvalue of its Laplacian matrix. Let ℐ n be the set of all trees of order n. In this paper, we will provide the ordering of trees in ℐ n up to the last eight trees according to their smallest algebraic connectivities when n ≥ 13. This extends the result of Shao et al.

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The smallest values of algebraic connectivity for trees

Abstract

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