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On the connectivity index of trees

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Abstract

The connectivity index χ1(G) of a graph G is the sum of the weights d(u)d(v) of all edges uv of G, where d(u) denotes the degree of the vertex u. Let T(n, r) be the set of trees on n vertices with diameter r. In this paper, we determine all trees in T(n, r) with the largest and the second largest connectivity index. Also, the trees in T(n, r) with the largest and the second largest connectivity index are characterized.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Yue Jiang & Mei Lu

Authors
  1. Yue Jiang
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  2. Mei Lu
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Corresponding author

Correspondence to Mei Lu.

Additional information

Mei Lu is partially supported by NNSFC (No. 10571105).

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Jiang, Y., Lu, M. On the connectivity index of trees. J Math Chem 43, 955–965 (2008). https://doi.org/10.1007/s10910-007-9281-3

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  • DOI: https://doi.org/10.1007/s10910-007-9281-3

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