Remoteness and distance eigenvalues of a graph

2015/07/25 by Huiqiu Lin, Lin, Huiqiu, Kinkar Ch. Das +3 · 1 citation
Mathematics · #05C50 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C50

paper · pdf · doi:10.48550/arxiv.1507.07083

9 pages

arxiv created 2015/07/25 · arxiv updated 2015/07/28

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

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