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Distance Degree Index of Some Derived Graphs

Department of Electronics and Information Engineering, Bozhou University, Bozhou 236800, China
School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
Department of Mathematics, University of the Punjab, Lahore 54590, Pakistan
Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54590, Pakistan
Department of Applied Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844, Iran
Authors to whom correspondence should be addressed.
Mathematics 2019, 7(3), 283;
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)
PDF [666 KB, uploaded 28 March 2019]


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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