On the Randić index

Authors:
Charles Delorme;Odile Favaron;Dieter Rautenbach
Affiliations:
LRI UMR 8623, Bât. 490, Université Paris-Sud, 91405 Orsay cedex, France;LRI UMR 8623, Bât. 490, Université Paris-Sud, 91405 Orsay cedex, France;Lehrstuhl II für Mathematik, RWTH Aachen, Aachen 52056, Germany
Venue:
Discrete Mathematics
Year:
2002

Citing 3
Cited 5

Some eigenvalue properties in graphs (conjectures of Graffiti. II)

Discrete Mathematics
Variable neighborhood search for extremal graphs: 1 the AutoGraphiX system

Discrete Mathematics
Wiener index versus maximum degree in trees

Discrete Applied Mathematics

A linear-programming approach to the generalized Randić index

Discrete Applied Mathematics
Closed formulas for the numbers of small independent sets and matchings and an extremal problem for trees

Discrete Applied Mathematics
Note: A proof of a conjecture on the Randić index of graphs with given girth

Discrete Applied Mathematics
Proof of the first part of the conjecture of Aouchiche and Hansen about the Randić index

Discrete Applied Mathematics
On a conjecture of the Randić index and the minimum degree of graphs

Discrete Applied Mathematics

Quantified Score

Hi-index	0.05

Visualization

Abstract

The Randić index R(G) of a graph G = (V, E) is the sum of (d(u)d(υ))-1/2 over all edges uυ ∈ E of G. Bollobás and Erdös (Ars Combin. 50 (1998) 225) proved that the Randić index of a graph of order n without isolated vertices is at least √n - 1. They asked for the minimum value of R(G) for graphs G with given minimum degree δ(G). We answer their question for δ(G) = 2 and propose a related conjecture. Furthermore, we prove a best-possible lower bound on the Randić index of a triangle-free graph G with given minimum degree δ(G).