The Least Algebraic Connectivity of Graphs

The Least Algebraic Connectivity of Graphs

The algebraic connectivity of a graph is defined as the second smallest eigenvalue of the Laplacian matrix of the graph, which is a parameter to measure how well a graph is connected. In this paper, we present two unique graphs whose algebraic connectivity attain the minimum among all graphs whose c...

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Main Authors: Guisheng Jiang, Guidong Yu, Jinde Cao
Format: Article
Language:English
Published: Hindawi Limited 2015-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2015/756960
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spelling doaj-18465c2f981449b0b5eab8a26c28ab6b2020-11-24T21:42:02ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/756960756960The Least Algebraic Connectivity of GraphsGuisheng Jiang0Guidong Yu1Jinde Cao2School of Physics and Electronic Engineering, Anqing Normal University, Anqing 246011, ChinaSchool of Mathematics and Computation Sciences, Anqing Normal University, Anqing 246011, ChinaDepartment of Mathematics, Southeast University, Nanjing, Jiangsu 210096, ChinaThe algebraic connectivity of a graph is defined as the second smallest eigenvalue of the Laplacian matrix of the graph, which is a parameter to measure how well a graph is connected. In this paper, we present two unique graphs whose algebraic connectivity attain the minimum among all graphs whose complements are trees, but not stars, and among all graphs whose complements are unicyclic graphs, but not stars adding one edge, respectively.http://dx.doi.org/10.1155/2015/756960
collection DOAJ
language English
format Article
sources DOAJ
author Guisheng Jiang
Guidong Yu
Jinde Cao
spellingShingle Guisheng Jiang
Guidong Yu
Jinde Cao
The Least Algebraic Connectivity of Graphs
Discrete Dynamics in Nature and Society
author_facet Guisheng Jiang
Guidong Yu
Jinde Cao
author_sort Guisheng Jiang
title The Least Algebraic Connectivity of Graphs
title_short The Least Algebraic Connectivity of Graphs
title_full The Least Algebraic Connectivity of Graphs
title_fullStr The Least Algebraic Connectivity of Graphs
title_full_unstemmed The Least Algebraic Connectivity of Graphs
title_sort least algebraic connectivity of graphs
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2015-01-01
description The algebraic connectivity of a graph is defined as the second smallest eigenvalue of the Laplacian matrix of the graph, which is a parameter to measure how well a graph is connected. In this paper, we present two unique graphs whose algebraic connectivity attain the minimum among all graphs whose complements are trees, but not stars, and among all graphs whose complements are unicyclic graphs, but not stars adding one edge, respectively.
url http://dx.doi.org/10.1155/2015/756960
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AT jindecao theleastalgebraicconnectivityofgraphs
AT guishengjiang leastalgebraicconnectivityofgraphs
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AT jindecao leastalgebraicconnectivityofgraphs
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