Czechoslovak Mathematical Journal

, Volume 68, Issue 1, pp 1–17 | Cite as

Graphs with small diameter determined by their D-spectra

  • Ruifang Liu
  • Jie Xue


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.


distance spectrum distance characteristic polynomial distance characteristic polynomial D-spectrum deter- mined by its D-spectrum 

MSC 2010



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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsZhengzhou UniversityHenanChina

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