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The (n,n)-graphs with the first three extremal Wiener indices

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Let G  =  (V, E) be a simple connected graph with vertex set V and edge set E. The Wiener index W(G) of G is the sum of distances between all pairs of vertices in G, i.e., \(W(G)=\sum_{\{u,v\}\subseteq{G}}^{\ }d_{G}(u,v)\), where d G (u, v) is the distance between vertices u and v in G. In this paper, we first give a new formula for calculating the Wiener index of an (n,n)-graph according its structure, and then characterize the (n,n)-graphs with the first three smallest and largest Wiener indices by this formula.

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Authors and Affiliations

  1. College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan, 410081, P. R. China

    Zikai Tang & Hanyuan Deng

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  1. Zikai Tang
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  2. Hanyuan Deng
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Correspondence to Hanyuan Deng.

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Tang, Z., Deng, H. The (n,n)-graphs with the first three extremal Wiener indices. J Math Chem 43, 60–74 (2008). https://doi.org/10.1007/s10910-006-9179-5

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  • DOI: https://doi.org/10.1007/s10910-006-9179-5

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