Distance Degree Index of Some Derived Graphs

Jianzhong Xu, Jia-Bao Liu, Ahsan Bilal, Uzma Ahmad, Hafiz Muhammad Afzal Siddiqui, Bahadur Ali and Muhammad Reza Farahani
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Jianzhong Xu: Department of Electronics and Information Engineering, Bozhou University, Bozhou 236800, China
Jia-Bao Liu: School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
Ahsan Bilal: Department of Mathematics, University of the Punjab, Lahore 54590, Pakistan
Uzma Ahmad: Department of Mathematics, University of the Punjab, Lahore 54590, Pakistan
Hafiz Muhammad Afzal Siddiqui: Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54590, Pakistan
Bahadur Ali: Department of Mathematics, University of the Punjab, Lahore 54590, Pakistan
Muhammad Reza Farahani: Department of Applied Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844, Iran

Mathematics, 2019, vol. 7, issue 3, 1-12

Abstract: Topological indices are numerical values associated with a graph (structure) that can predict many physical, chemical, and pharmacological properties of organic molecules and chemical compounds. The distance degree ( D D ) index was introduced by Dobrynin and Kochetova in 1994 for characterizing alkanes by an integer. In this paper, we have determined expressions for a D D index of some derived graphs in terms of the parameters of the parent graph. Specifically, we establish expressions for the D D index of a line graph, subdivision graph, vertex-semitotal graph, edge-semitotal graph, total graph, and paraline graph.

Keywords: DD index; Wiener index; Edge Wiener; degree of a vertex; distance between two vertices (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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