2015/05/28 by Ruifang Liu, Jie Xue, Liu, Ruifang +1
Computer Science · Mathematics · #05C50 #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.1505.07651
openalex publication_date 2015/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a connected graph with vertex set V(G)=\v1,v2,...,vn\. The distance matrix D(G)=(dij)n× n is the matrix indexed by the vertices of G, where dij denotes the distance between the vertices vi and vj. Suppose that λ1(D)≥λ2(D)≥⋯≥λn(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. In this paper, we give the distance characteristic polynomial of some graphs with small diameter, and also prove that these graphs are determined by their D-spectra.