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The Signless Laplacian or Adjacency Spectral Radius of Bicyclic Graphs with Given Number of Cut Edges

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Abstract

Let \(\fancyscript{B}(n,r)\) be the set of all bicyclic graphs with \(n\) vertices and \(r\) cut edges. In this paper we determine the unique graph with maximal adjacency spectral radius or signless Laplacian spectral radius among all graphs in \(\fancyscript{B}(n,r)\).

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Acknowledgments

We greatly thank the referees for careful reading and helpful suggestions that led to many improvements.

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Authors and Affiliations

  1. School of Mathematical Sciences, Anhui University, Hefei, 230601, People’s Republic of China

    Zhen-Mu Hong & Yi-Zheng Fan

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  1. Zhen-Mu Hong
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  2. Yi-Zheng Fan
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Correspondence to Yi-Zheng Fan.

Additional information

Supported by National Natural Science Foundation of China (11071002, 11371028), Program for New Century Excellent Talents in University (NCET-10-0001), Key Project of Chinese Ministry of Education (210091), Specialized Research Fund for the Doctoral Program of Higher Education (20103401110002), Scientific Research Fund for Fostering Distinguished Young Scholars of Anhui University (KJJQ1001).

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Hong, ZM., Fan, YZ. The Signless Laplacian or Adjacency Spectral Radius of Bicyclic Graphs with Given Number of Cut Edges. Graphs and Combinatorics 31, 1473–1485 (2015). https://doi.org/10.1007/s00373-014-1477-2

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  • DOI: https://doi.org/10.1007/s00373-014-1477-2

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