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Eigenvalues and diameter

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Abstract

Let G be a connected graph of order n. The diameter of a graph is the maximum distance between any two vertices of G. In this paper, we will give some bounds on the diameter of G in terms of eigenvalues of adjacency matrix and Laplacian matrix, respectively.

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Authors and Affiliations

  1. School of Mathematics and Computer Science, Hubei University, Wuhan, 430062, P. R. China

    Hui Qing Liu

  2. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, P. R. China

    Mei Lu

Authors
  1. Hui Qing Liu
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  2. Mei Lu
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Correspondence to Hui Qing Liu.

Additional information

The first author is partially supported by National Natural Science Foundation of China (Grant Nos. 10971114, 10671081), NSF and Innovation Group Fund of Hubei Provincial Department of Education (Grant Nos. D20081005, T200901) and Open Research Fund of Hubei Key Laboratory of Applied Mathematics; the second author is partially supported by National Natural Science Foundation of China (Grant Nos. 10971114, 10990011)

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Liu, H.Q., Lu, M. Eigenvalues and diameter. Acta. Math. Sin.-English Ser. 27, 1107–1114 (2011). https://doi.org/10.1007/s10114-011-8681-2

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  • DOI: https://doi.org/10.1007/s10114-011-8681-2

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