The Largest Normalized Laplacian Spectral Radius of Non-Bipartite Graphs

Ji Ming Guo; Jianxi Li; Wai Chee Shiu

doi:10.1007/s40840-015-0241-y

The Largest Normalized Laplacian Spectral Radius of Non-Bipartite Graphs

Ji Ming Guo, Jianxi Li, Wai Chee Shiu^*

^*Corresponding author for this work

Department of Mathematics

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

6 Citations (Scopus)

Abstract

In this paper, we firstly consider how the normalized Laplacian spectral radius of a non-bipartite graph behaves by several graph operations. As applications of the result, the largest normalized Laplacian spectral radius of non-bipartite unicyclic graphs with fixed order and girth is determined. Moreover, the largest normalized Laplacian spectral radius among non-bipartite unicyclic graphs with fixed girth and order is also determined. The maximizer is the tadpole graph with the same (odd) girth.

Original language	English
Pages (from-to)	77-87
Number of pages	11
Journal	Bulletin of the Malaysian Mathematical Sciences Society
Volume	39
Issue number	supplement 1
Early online date	19 Nov 2015
DOIs	https://doi.org/10.1007/s40840-015-0241-y
Publication status	Published - Jun 2016

User-Defined Keywords

Non-bipartite graph
Normalized Laplacian spectral radius
Unicyclic graph

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10.1007/s40840-015-0241-y

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title = "The Largest Normalized Laplacian Spectral Radius of Non-Bipartite Graphs",

abstract = "In this paper, we firstly consider how the normalized Laplacian spectral radius of a non-bipartite graph behaves by several graph operations. As applications of the result, the largest normalized Laplacian spectral radius of non-bipartite unicyclic graphs with fixed order and girth is determined. Moreover, the largest normalized Laplacian spectral radius among non-bipartite unicyclic graphs with fixed girth and order is also determined. The maximizer is the tadpole graph with the same (odd) girth.",

keywords = "Non-bipartite graph, Normalized Laplacian spectral radius, Unicyclic graph",

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

note = "Funding information: This paper was partially supported by General Research Fund of Hong Kong; Faculty Research Grant of Hong Kong Baptist University; NSF of China (Nos. 11371372, 11101358); NSF of Fujian (Nos. 2011J05014, 2011J01026); and Project of Fujian Education Department (No. JA11165). Publisher copyright: Copyright {\textcopyright} 2015, Malaysian Mathematical Sciences Society and Universiti Sains Malaysia",

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AU - Li, Jianxi

AU - Shiu, Wai Chee

N1 - Funding information: This paper was partially supported by General Research Fund of Hong Kong; Faculty Research Grant of Hong Kong Baptist University; NSF of China (Nos. 11371372, 11101358); NSF of Fujian (Nos. 2011J05014, 2011J01026); and Project of Fujian Education Department (No. JA11165). Publisher copyright: Copyright © 2015, Malaysian Mathematical Sciences Society and Universiti Sains Malaysia

PY - 2016/6

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N2 - In this paper, we firstly consider how the normalized Laplacian spectral radius of a non-bipartite graph behaves by several graph operations. As applications of the result, the largest normalized Laplacian spectral radius of non-bipartite unicyclic graphs with fixed order and girth is determined. Moreover, the largest normalized Laplacian spectral radius among non-bipartite unicyclic graphs with fixed girth and order is also determined. The maximizer is the tadpole graph with the same (odd) girth.

AB - In this paper, we firstly consider how the normalized Laplacian spectral radius of a non-bipartite graph behaves by several graph operations. As applications of the result, the largest normalized Laplacian spectral radius of non-bipartite unicyclic graphs with fixed order and girth is determined. Moreover, the largest normalized Laplacian spectral radius among non-bipartite unicyclic graphs with fixed girth and order is also determined. The maximizer is the tadpole graph with the same (odd) girth.

KW - Non-bipartite graph

KW - Normalized Laplacian spectral radius

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JF - Bulletin of the Malaysian Mathematical Sciences Society

IS - supplement 1

ER -

The Largest Normalized Laplacian Spectral Radius of Non-Bipartite Graphs

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