On the Wiener polarity index of graphs

Hongbo Hua and Kinkar Ch. Das

Applied Mathematics and Computation, 2016, vol. 280, issue C, 162-167

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.

Keywords: The Wiener polarity index; Diameter; Independence number; The Zagreb indices; Hosoya index; Nordhaus–Gaddum-type inequality (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:280:y:2016:i:c:p:162-167

DOI: 10.1016/j.amc.2016.01.043

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