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J Inequal Appl. 2017;2017(1):305. doi: 10.1186/s13660-017-1579-5. Epub 2017 Dec 13.

On the bounds of degree-based topological indices of the Cartesian product of F-sum of connected graphs.

Author information

Department of Mathematical Sciences, United Arab Emirates University, P. O. Box 15551, Al Ain, United Arab Emirates.
Department of Mathematics, School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Sector H-12, Islamabad, Pakistan.
Department of Mathematics, Government College University Faisalabad (GCUF), Jhang Road, Faisalabad, Punjab Pakistan.
Department of Mathematics, COMSATS Institute of Information Technology (CIIT), Defence Road, Off Raiwind Road, Lahore, Punjab Pakistan.


Topological indices are the mathematical tools that correlate the chemical structure with various physical properties, chemical reactivity or biological activity numerically. A topological index is a function having a set of graphs as its domain and a set of real numbers as its range. In QSAR/QSPR study, a prediction about the bioactivity of chemical compounds is made on the basis of physico-chemical properties and topological indices such as Zagreb, Randić and multiple Zagreb indices. In this paper, we determine the lower and upper bounds of Zagreb indices, the atom-bond connectivity (ABC) index, multiple Zagreb indices, the geometric-arithmetic (GA) index, the forgotten topological index and the Narumi-Katayama index for the Cartesian product of F-sum of connected graphs by using combinatorial inequalities.


ABC-index; Cartesian product; F-index; F-sum; GA-index; Zagreb index

Conflict of interest statement

The authors declare that they have no competing interests.

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