Graphs and Combinatorics

, Volume 27, Issue 2, pp 215–229 | Cite as

Algebraic Connectivity of Connected Graphs with Fixed Number of Pendant Vertices

  • Arbind Kumar Lal
  • Kamal Lochan Patra
  • Binod Kumar Sahoo
Original Paper

Abstract

In this paper, we consider the following problem. Over the class of all simple connected graphs of order n with k pendant vertices (n, k being fixed), which graph maximizes (respectively, minimizes) the algebraic connectivity? We also discuss the algebraic connectivity of unicyclic graphs.

Keywords

Laplacian matrix Algebraic connectivity Characteristic set Perron component Pendant vertex 

Mathematics Subject Classification (2000)

05C50 

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Copyright information

© Springer 2010

Authors and Affiliations

  • Arbind Kumar Lal
    • 1
  • Kamal Lochan Patra
    • 2
  • Binod Kumar Sahoo
    • 2
  1. 1.Department of Mathematics and StatisticsIndian Institute of Technology KanpurKanpurIndia
  2. 2.School of Mathematical SciencesNational Institute of Science Education and ResearchBhubaneswarIndia

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