On the Wiener polarity index of graphs

Hongbo Hua; Kinkar Ch Das

doi:10.1016/j.amc.2016.01.043

On the Wiener polarity index of graphs

Hongbo Hua, Kinkar Ch Das

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

Abstract

The Wiener polarity index W_p(G) of a graph G is the number of unordered pairs of vertices {u, v} in G such that the distance between u and v is equal to 3. Very recently, Zhang and Hu studied the Wiener polarity index in [Y. Zhang, Y. Hu, 2016] [38]. In this short paper, we establish an upper bound on the Wiener polarity index in terms of Hosoya index and characterize the corresponding extremal graphs. Moreover, we obtain Nordhaus-Gaddum-type results for W_p(G). Our lower bound on _Wp(G)+_Wp(G¯) is always better than the previous lower bound given by Zhang and Hu.

Original language	English
Pages (from-to)	162-167
Number of pages	6
Journal	Applied Mathematics and Computation
Volume	280
DOIs	https://doi.org/10.1016/j.amc.2016.01.043
State	Published - 20 Apr 2016

Keywords

Diameter
Hosoya index
Independence number
Nordhaus-Gaddum-type inequality
The Wiener polarity index
The Zagreb indices

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10.1016/j.amc.2016.01.043

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title = "On the Wiener polarity index of graphs",

abstract = "The Wiener polarity index Wp(G) of a graph G is the number of unordered pairs of vertices \{u, v\} in G such that the distance between u and v is equal to 3. Very recently, Zhang and Hu studied the Wiener polarity index in [Y. Zhang, Y. Hu, 2016] [38]. In this short paper, we establish an upper bound on the Wiener polarity index in terms of Hosoya index and characterize the corresponding extremal graphs. Moreover, we obtain Nordhaus-Gaddum-type results for Wp(G). Our lower bound on Wp(G)+Wp(G¯) is always better than the previous lower bound given by Zhang and Hu.",

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AU - Das, Kinkar Ch

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AB - The Wiener polarity index Wp(G) of a graph G is the number of unordered pairs of vertices {u, v} in G such that the distance between u and v is equal to 3. Very recently, Zhang and Hu studied the Wiener polarity index in [Y. Zhang, Y. Hu, 2016] [38]. In this short paper, we establish an upper bound on the Wiener polarity index in terms of Hosoya index and characterize the corresponding extremal graphs. Moreover, we obtain Nordhaus-Gaddum-type results for Wp(G). Our lower bound on Wp(G)+Wp(G¯) is always better than the previous lower bound given by Zhang and Hu.

KW - Diameter

KW - Hosoya index

KW - Independence number

KW - Nordhaus-Gaddum-type inequality

KW - The Wiener polarity index

KW - The Zagreb indices

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DO - 10.1016/j.amc.2016.01.043

M3 - Article

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SN - 0096-3003

VL - 280

SP - 162

EP - 167

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

On the Wiener polarity index of graphs

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Keywords

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