Received: 10 July 2018 / Revised: 7 August 2018 / Accepted: 9 August 2018 / Published: 17 August 2018

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**Abstract**

In this article, we study the chemical graph of a cyclic octahedron structure of dimension

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*n*and compute the eccentric connectivity polynomial, the eccentric connectivity index, the total eccentricity, the average eccentricity, the first Zagreb index, the second Zagreb index, the third Zagreb
In this article, we study the chemical graph of a cyclic octahedron structure of dimension

*n*and compute the eccentric connectivity polynomial, the eccentric connectivity index, the total eccentricity, the average eccentricity, the first Zagreb index, the second Zagreb index, the third Zagreb index, the atom bond connectivity index and the geometric arithmetic index of the cyclic octahedron structure. Furthermore, we give the analytically closed formulas of these indices which are helpful for studying the underlying topologies. Full article