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Mathematics 2019, 7(3), 283; https://doi.org/10.3390/math7030283

Distance Degree Index of Some Derived Graphs

1
Department of Electronics and Information Engineering, Bozhou University, Bozhou 236800, China
2
School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
3
Department of Mathematics, University of the Punjab, Lahore 54590, Pakistan
4
Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54590, Pakistan
5
Department of Applied Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844, Iran
*
Authors to whom correspondence should be addressed.
Received: 21 January 2019 / Revised: 4 March 2019 / Accepted: 14 March 2019 / Published: 19 March 2019
(This article belongs to the Special Issue Graph-Theoretic Problems and Their New Applications)
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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. View Full-Text
Keywords: DD index; Wiener index; Edge Wiener; degree of a vertex; distance between two vertices DD index; Wiener index; Edge Wiener; degree of a vertex; distance between two vertices
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Xu, J.; Liu, J.-B.; Bilal, A.; Ahmad, U.; Siddiqui, H.M.A.; Ali, B.; Farahani, M.R. Distance Degree Index of Some Derived Graphs. Mathematics 2019, 7, 283.

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