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Mathematics 2019, 7(4), 324; https://doi.org/10.3390/math7040324

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.
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)
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PDF [273 KB, uploaded 1 April 2019]

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. View Full-Text
Keywords: extremal values; PI index; k-trees; distance extremal values; PI index; k-trees; distance
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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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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