2020/10/05 by Chen Xu, Chen, Xu, Guoping Wang +1
Chemistry · Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #Synthesis and Properties of Aromatic Compounds
paper · pdf · doi:10.48550/arxiv.2010.02760
openalex publication_date 2020/10/05 · openalex created_date 2020/10/15 · openalex updated_date 2026/07/28
Suppose that G is a connected simple graph with the vertex set V( G ) = \ v1,v2,⋯ ,vn \ . Let d( vi,vj ) be the distance between vi and vj. Then the distance matrix of G is D( G ) =( dij )n× n, where dij=d( vi,vj ) . Since D( G ) is a non-negative real symmetric matrix, its eigenvalues can be arranged λ1(G)≥ λ2(G)≥ ⋯ ≥ λn(G), where eigenvalues λ1(G) and λn(G) are called the distance spectral radius and the least distance eigenvalue of G, respectively. The \it diameter of graph G is the farthest distance between all pairs of vertices. In this paper, we determine the unique graph whose distance spectral radius attains maximum and minimum among all complements of graphs of diameter greater than three, respectively. Furthermore, we also characterize the unique graph whose least distance eigenvalue attains maximum and minimum among all complements of graphs of diameter greater than three, respectively.