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Algebraic Connectivity of Connected Graphs with Fixed Number of Pendant Vertices

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.

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Correspondence to Arbind Kumar Lal.

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A. K. Lal takes this opportunity to thank the Department of Science and Technology, New Delhi, India, for the project grant.

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Lal, A.K., Patra, K.L. & Sahoo, B.K. Algebraic Connectivity of Connected Graphs with Fixed Number of Pendant Vertices. Graphs and Combinatorics 27, 215–229 (2011). https://doi.org/10.1007/s00373-010-0975-0

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  • DOI: https://doi.org/10.1007/s00373-010-0975-0

Keywords

  • Laplacian matrix
  • Algebraic connectivity
  • Characteristic set
  • Perron component
  • Pendant vertex

Mathematics Subject Classification (2000)

  • 05C50