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# The modified Schultz index of graph operations

### Abstract

creative_2017_26_1_53_60_abstract

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creative_2017_26_1_53_60

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Given a simple and connected graph with vertex set , denoting by , the degree of a vertex and by the distance of two vertices, the modified Schultz index of is given by where the summation goes over all non ordered pairs of vertices of .
In this paper we consider some graph operations, namely cartesian product, complete product, composition and subdivision, and we obtain explicit formulae for the modified Schultz index of a graph in terms of the number of vertices and edges as well as some other topological invariants such as the Wiener index, the Schultz index and the first and second Zagreb indices.