The orderings of bicyclic graphs and connected graphs by algebraic connectivity
type: Item
instance of: scholarly article
title: The orderings of bicyclic graphs and connected graphs by algebraic connectivity
zbMATH Open document ID: 1204.05056
author: Jiming Guo
author: Wai Chee Shiu
author: Jianxi Li
published in: The Electronic Journal of Combinatorics
publication date: 2010-12-16T00:00:00Z
full work available at URL: https://eudml.org/doc/227778
full work available at URL: v17i1r162.html
review text: Summary: The algebraic connectivity of a graph \(G\) is the second smallest eigenvalue of its Laplacian matrix. Let \({\mathcal B}_n\) be the set of all bicyclic graphs of order \(n\). In this paper we determine the last four bicyclic graphs (according to their smallest algebraic connectivities) among all graphs in \({\mathcal B}_n\) when \(n\geq 13\). This result, together with our previous results on trees and unicyclic graphs, can be used to further determine the last sixteen graphs among all connected graphs of order \(n\). This extends the results of \textit{J.-Y. Shao, J.-M. Guo} and \textit{H.-Y. Shan} [Linear Algebra Appl. 428, No. 7, 1421--1438 (2008; Zbl 1134.05063)].
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 05C38
zbMATH DE Number: 5827411
zbMATH Keywords: bicyclic graph
zbMATH Keywords: connected graph
zbMATH Keywords: algebraic connectivity
zbMATH Keywords: order
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5827411