Relation between Randić Index and Average Distance of Trees
نویسندگان
چکیده
The Randić index R(G) of a graph G is the sum of weights (deg(u) deg(v))−0.5 over all edges uv of G, where deg(v) denotes the degree of a vertex v. We prove that for any tree T with n1 leaves R(T ) ≥ ad(T ) + max(0,n1 − 2), where ad(T ) is the average distance between vertices of T . As a consequence we resolve the conjecture R(G) ≥ ad(G) given by Fajtlowicz in 1988 for the case when G is a tree.
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