Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10678334 | Applied Mathematics Letters | 2011 | 5 Pages |
Abstract
The RandiÄ index R(G) of a graph G is defined by R(G)=âuv1d(u)d(v), where d(u) is the degree of a vertex u in G and the summation extends over all edges uv of G. Aouchiche et al. proposed a conjecture on the relationship between the RandiÄ index and the diameter: for any connected graph on nâ¥3 vertices with the RandiÄ index R(G) and the diameter D(G), R(G)âD(G)â¥2ân+12andR(G)D(G)â¥nâ3+222nâ2, with equalities if and only if G is a path. In this work, we show that this conjecture is true for trees. Furthermore, we prove that for any connected graph on nâ¥3 vertices with the RandiÄ index R(G) and the diameter D(G), R(G)âD(G)â¥2ân+12, with equality if and only if G is a path.
Keywords
Related Topics
Physical Sciences and Engineering
Engineering
Computational Mechanics
Authors
Jianxi Liu, Meili Liang, Bo Cheng, Bolian Liu,