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

被引：15

作者：

Wang, Shaohui ^{[1
]}

Shao, Zehui ^{[2
]}

Liu, Jia-Bao ^{[3
]}

Wei, Bing ^{[4
]}

机构：

[1] Texas A&M Int Univ, Dept Math & Phys, Laredo, TX 78041 USA

[2] Guangzhou Univ, Inst Comp Sci & Technol, Guangzhou 510006, Guangdong, Peoples R China

[3] Anhui Jianzhu Univ, Sch Math & Phys, Hefei 230601, Anhui, Peoples R China

[4] Univ Mississippi, Dept Math, University, MS 38677 USA

来源：

MATHEMATICS | 2019年 / 7卷 / 04期

关键词：

extremal values; PI index; k-trees; distance; MAXIMUM ABC INDEX; PI INDEX; ZAGREB INDEXES; GRAPHS; PRODUCT; SQUARES; SUM;

D O I：

10.3390/math7040324

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Padmakar-Ivan (PI) index is a distance-based topological index and a molecular structure descriptor, which is the sum of the number of vertices over all edges uv of a graph such that these vertices are not equidistant from u and v. In this paper, we explore the results of PI-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 PI-values on some classes of k-trees and compare them, and our results extend and enrich some known conclusions.

引用

页数：10

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