The orderings of bicyclic graphs and connected graphs by algebraic connectivity

Jianxi Li*, Ji Ming Guo, Wai Chee Shiu

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

5 Citations (Scopus)


The algebraic connectivity of a graph G is the second smallest eigenvalue of its Laplacian matrix. Let Bn 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 Bn when n ≥ 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 Shao et al.

Original languageEnglish
Article numberR162
Number of pages11
JournalElectronic Journal of Combinatorics
Issue number1
Publication statusPublished - 3 Dec 2010

Scopus Subject Areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Algebraic connectivity
  • Bicyclic graph
  • Connected graph
  • Order


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