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Graphs with small diameter determined by their D-spectra

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Abstract

Let G be a connected graph with vertex set V(G) = {v1, v2,..., v n }. The distance matrix D(G) = (d ij )n×n is the matrix indexed by the vertices of G, where d ij denotes the distance between the vertices v i and v j . Suppose that λ1(D) ≥ λ2(D) ≥... ≥ λ n (D) are the distance spectrum of G. The graph G is said to be determined by its D-spectrum if with respect to the distance matrix D(G), any graph having the same spectrum as G is isomorphic to G. We give the distance characteristic polynomial of some graphs with small diameter, and also prove that these graphs are determined by their D-spectra.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Zhengzhou University, 100 Ke Xue Road, Zhengzhou, 450001, Henan, China

    Ruifang Liu & Jie Xue

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  1. Ruifang Liu
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  2. Jie Xue
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Correspondence to Ruifang Liu.

Additional information

Supported by National Natural Science Foundation of China (No. 11571323), Outstanding Young Talent Research Fund of Zhengzhou University (No. 1521315002), the China Postdoctoral Science Foundation (No. 2017M612410) and Foundation for University Key Teacher of Henan Province (No. 2016GGJS-007).

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Liu, R., Xue, J. Graphs with small diameter determined by their D-spectra. Czech Math J 68, 1–17 (2018). https://doi.org/10.21136/CMJ.2018.0505-15

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  • DOI: https://doi.org/10.21136/CMJ.2018.0505-15

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