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On the spectral spread of bicyclic graphs with given girth

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Abstract

The spectral spread of a graph is defined to be the difference between the largest and the least eigenvalue of the adjacency matrix of the graph. A graph G is said to be bicyclic, if G is connected and |E(G)| = |V (G)| + 1. Let B(n, g) be the set of bicyclic graphs on n vertices with girth g. In this paper some properties about the least eigenvalues of graphs are given, by which the unique graph with maximal spectral spread in B(n, g) is determined.

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Authors and Affiliations

  1. School of Mathematical Science, Chuzhou University, Anhui, Chuzhou, 239012, China

    Bing Wang & Ming-qing Zhai

  2. Department of Mathematics, East China Normal University, Shanghai, 200241, China

    Jin-long Shu

Authors
  1. Bing Wang
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  2. Ming-qing Zhai
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  3. Jin-long Shu
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Corresponding author

Correspondence to Ming-qing Zhai.

Additional information

Supported by the National Natural Science Foundation of China (No.11101057), China Postdoctoral Science Foundation (No.20110491443), the NSF of Education Ministry of Anhui province (No.KJ2012Z283) and Scientific Research Foundation of Chuzhou University (No.2011kj004B).

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Wang, B., Zhai, Mq. & Shu, Jl. On the spectral spread of bicyclic graphs with given girth. Acta Math. Appl. Sin. Engl. Ser. 29, 517–528 (2013). https://doi.org/10.1007/s10255-013-0228-0

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  • DOI: https://doi.org/10.1007/s10255-013-0228-0

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