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Open AccessArticle

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

1
Department of Mathematics and Physics, Texas A&M International University, Laredo, TX 78041, USA
2
Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China
3
School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
4
Department of Mathematics, The University of Mississippi, University, MS 38677, USA
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(4), 324; https://doi.org/10.3390/math7040324
Received: 26 January 2019 / Revised: 11 March 2019 / Accepted: 11 March 2019 / Published: 1 April 2019
(This article belongs to the Special Issue Graph-Theoretic Problems and Their New Applications)
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. View Full-Text
Keywords: extremal values; PI index; k-trees; distance extremal values; PI index; k-trees; distance
MDPI and ACS Style

Wang, S.; Shao, Z.; Liu, J.-B.; Wei, B. The Bounds of Vertex Padmakar–Ivan Index on k-Trees. Mathematics 2019, 7, 324.

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