On a conjecture of the Randić index

Authors:
Zhifu You;Bolian Liu
Affiliations:
Department of Mathematics, South China Normal University, Guangzhou, 510631, PR China;Department of Mathematics, South China Normal University, Guangzhou, 510631, PR China
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

The Randic index of a graph G is defined as R(G)=@?"u"~"v(d(u)d(v))^-^1^2, where d(u) is the degree of vertex u and the summation goes over all pairs of adjacent vertices u, v. A conjecture on R(G) for connected graph G is as follows: R(G)=r(G)-1, where r(G) denotes the radius of G. We proved that the conjecture is true for biregular graphs, connected graphs with order n@?10 and tricyclic graphs.