Distance and distance signless Laplacian spread of connected graphs

2016/07/02 by Lihua You, Liyong Ren, You, Lihua +3 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics (math.CO) #Complex Network Analysis Techniques #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.1607.00473

openalex publication_date 2016/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a connected graph G on n vertices, recall that the distance signless Laplacian matrix of G is defined to be Q(G)=Tr(G)+D(G), where D(G) is the distance matrix, Tr(G)=diag(D₁, D₂, …, D_n) and D_i is the row sum of D(G) corresponding to vertex v_i. Denote by ρ^D(G), ρ_min^D(G) the largest eigenvalue and the least eigenvalue of D(G), respectively. And denote by q^D(G), q_min^D(G) the largest eigenvalue and the least eigenvalue of Q(G), respectively. The distance spread of a graph G is defined as S_D(G)=ρ^D(G)- ρ_min^D(G), and the distance signless Laplacian spread of a graph G is defined as S_Q(G)=q^D(G)-q_min^D(G). In this paper, we point out an error in the result of Theorem 2.4 in "Distance spectral spread of a graph" [G.L. Yu, et al, Discrete Applied Mathematics. 160 (2012) 2474--2478] and rectify it. As well, we obtain some lower bounds on ddistance signless Laplacian spread of a graph.

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