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Algebraic Connectivity of Connected Graphs with Fixed Number of Pendant Vertices

Graphs and Combinatorics volume 27, pages 215–229 (2011)Cite this article

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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Authors and Affiliations

  1. Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, 208016, India

    Arbind Kumar Lal

  2. School of Mathematical Sciences, National Institute of Science Education and Research, Bhubaneswar, 751005, India

    Kamal Lochan Patra & Binod Kumar Sahoo

Authors
  1. Arbind Kumar Lal
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  2. Kamal Lochan Patra
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  3. Binod Kumar Sahoo
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Correspondence to Arbind Kumar Lal.

Additional information

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