The Bounds of Vertex Padmakar–Ivan Index on k -Trees

Shaohui Wang, Zehui Shao, Jia-Bao Liu and Bing Wei
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Shaohui Wang: Department of Mathematics and Physics, Texas A&M International University, Laredo, TX 78041, USA
Zehui Shao: Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China
Jia-Bao Liu: School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
Bing Wei: Department of Mathematics, The University of Mississippi, University, MS 38677, USA

Mathematics, 2019, vol. 7, issue 4, 1-10

Abstract: The Padmakar–Ivan ( P I ) index is a distance-based topological index and a molecular structure descriptor, which is the sum of the number of vertices over all edges u v of a graph such that these vertices are not equidistant from u and v . In this paper, we explore the results of P I -indices from trees to recursively clustered trees, the k -trees. Exact sharp upper bounds of PI indices on k -trees are obtained by the recursive relationships, and the corresponding extremal graphs are given. In addition, we determine the P I -values on some classes of k -trees and compare them, and our results extend and enrich some known conclusions.

Keywords: extremal values; PI index; k -trees; distance (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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