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Maximum Spectral Radius of Graphs with Connectivity at Most k and Minimum Degree at Least δ

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Combinatorial Algorithms (IWOCA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8288))

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Abstract

Li, Shiu, Chan and Chang [On the spectral radius of graphs with connectivity at most k, J. Math. Chem., 46 (2009), 340-346] studied the spectral radius of graphs of order n with κ(G) ≤ k and showed that among those graphs, the maximum spectral radius is obtained uniquely at \(K_k^n\), which is the graph obtained by joining k edges from k vertices of K n − 1 to an isolated vertex. In this paper, we study the spectral radius of graphs of order n with κ(G) ≤ k and minimum degree δ(G) ≥ k . We show that among those graphs, the maximum spectral radius is obtained uniquely at K k  + (K δ − k + 1 ∪ K n − δ − 1).

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Author information

Authors and Affiliations

  1. Department of Mathematics, Xi’an Jiaotong University, Xi’an, 710049, P.R. China

    Hongliang Lu

  2. School of Electrical Engineering and Computer Science, The University of Newcastle, Newcastle, Australia

    Yuqing Lin

Authors
  1. Hongliang Lu
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  2. Yuqing Lin
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Editor information

Editors and Affiliations

  1. UFR des Sciences et Techniques, LITIS, Université de Rouen, 76821, EA 4180, Mont Saint Aignan Cedex, France

    Thierry Lecroq  & Laurent Mouchard  & 

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Lu, H., Lin, Y. (2013). Maximum Spectral Radius of Graphs with Connectivity at Most k and Minimum Degree at Least δ . In: Lecroq, T., Mouchard, L. (eds) Combinatorial Algorithms. IWOCA 2013. Lecture Notes in Computer Science, vol 8288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45278-9_25

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  • DOI: https://doi.org/10.1007/978-3-642-45278-9_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-45277-2

  • Online ISBN: 978-3-642-45278-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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