a b s t r a c tThe Wiener index is the sum of distances between all vertex pairs in a connected graph. This notion was motivated by various mathematical properties and chemical applications. In this paper we introduce four new operations on graphs and study the Wiener indices of the resulting graphs.

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The study of topological indices -graph invariants that can be used for describing and predicting physicochemical or pharmacological properties of organic compounds -is currently one of the most active research fields in chemical graph theory. In this paper we study the Schultz index and find a relation with the Wiener index of the armchair polyhex nanotubes T U V C 6 [2p, q]. An exact expression for Schultz index of this molecule is also found.

a b s t r a c tThe ordinary generalized geometric-arithmetic index of graphs is introduced and some properties especially lower and upper bounds in terms of other graph invariants and topological indices are obtained.