Continuing the recent work of L. Zhong and K. Xu [MATCH Commun. Math. Comput. Chem.71(2014) 627-642], we determine inequalities among several vertex-degree-based topological indices; first geometric-arithmetic index(GA), augmented Zagreb index (AZI), Randi$acute{c}$ index (R), atom-bond connectivity index (ABC), sum-connectivity index (X)and harmonic index (H).
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