The smallest values of algebraic connectivity for unicyclic graphs

Jianxi Li, Ji Ming Guo, Wai Chee SHIU

Research output: Contribution to journalJournal articlepeer-review

11 Citations (Scopus)


The algebraic connectivity of G is the second smallest eigenvalue of its Laplacian matrix. Let un be the set of all unicyclic graphs of order n. In this paper, we will provide the ordering of unicyclic graphs in u n up to the last seven graphs according to their algebraic connectivities when n≥13. This extends the results of Liu and Liu [Y. Liu, Y. Liu, The ordering of unicyclic graphs with the smallest algebraic connectivity, Discrete Math. 309 (2009) 4315-4325] and Guo [J.-M. Guo, A conjecture on the algebraic connectivity of connected graphs with fixed girth, Discrete Math. 308 (2008) 5702-5711].

Original languageEnglish
Pages (from-to)1633-1643
Number of pages11
JournalDiscrete Applied Mathematics
Issue number15
Publication statusPublished - 6 Aug 2010

Scopus Subject Areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

User-Defined Keywords

  • Algebraic connectivity
  • Order
  • Unicyclic graph


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