Remoteness and distance eigenvalues of a graph

2015/07/25 by Lin, Huiqiu, Das, Kinkar Ch., Wu, Baoyindureng · 1 citation
#05C50 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1507.07083

Abstract

Let G be a connected graph of order n with diameter d. Remoteness ρ of G is the maximum average distance from a vertex to all others and ∂₁≥⋯≥ ∂_n are the distance eigenvalues of G. In \citeAH, Aouchiche and Hansen conjectured that ρ+∂₃>0 when d≥ 3 and ρ+∂_{\lfloor(7d)/(8)\rfloor}>0. In this paper, we confirm these two conjectures. Furthermore, we give lower bounds on ∂_n+ρ and ∂₁-ρ when G\ncong K_n and the extremal graphs are characterized.

Cited by

• On Proximity and other Distance Parameters in Planar Graphs

Related

• Remoteness of graphs with given size and connectivity constraints
• The least distance eigenvalue of the complements of graphs of diameter greater than three
• Proximity and Remoteness in Graphs: a survey
• Graphs with at most three distance eigenvalues different from -1 and -2
• More results on the distance (signless) Laplacian eigenvalues of graphs