Remarks on lower bounds of the general Randi´c index R????1 of graph

Abstract

Let G = (V, E), V = f1, 2, . . . , ng be a simple graph with n 2 vertices and m edges with vertex
degree sequence d1 d2 dn. Topological degree–based index of graph Rα =
Σ
ij(didj)α, where i j
denotes that vertices i and j are adjacent, is referred to as general Randi´c index. We consider the case when
α = ????1 and obtain lower bound for R????1 and lower and upper bounds of normalized Laplacian eigenvalues