Bounds on the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml22" display="inline" overflow="scroll" altimg="si22.gif"><mml:mi>P</mml:mi><mml:mi>I</mml:mi></mml:math> index of unicyclic and bicyclic graphs with given girth

Gang, Ma; Bian, Qiuju; Wang, Jianfeng

doi:10.1016/j.dam.2017.06.011

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“…Nowadays, Padmakar-Ivan indices are widely used in Quantitative Structure-Activity Relationship (QSAR) and Quantitative Structure-Property Relationship (QSPR) [5,6], and there are many interesting results [5,[7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] between graph theory and chemistry. For instances, Klavzar [27] provided PI-partitions and arbitrary Cartesian product.…”

Section: Introductionmentioning

confidence: 99%

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

2019

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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.

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