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Minimum sum-connectivity indices of trees and unicyclic graphs of a given matching number

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Abstract

The sum-connectivity index is a newly proposed molecular descriptor defined as the sum of the weights of the edges of the graph, where the weight of an edge uv of the graph, incident to vertices u and v, having degrees d u and d v is (d u  + d v )−1/2. We obtain the minimum sum-connectivity indices of trees and unicyclic graphs with given number of vertices and matching number, respectively, and determine the corresponding extremal graphs. Additionally, we deduce the n-vertex unicyclic graphs with the first and second minimum sum-connectivity indices for n ≥ 4.

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Authors and Affiliations

  1. Department of Mathematics, South China Normal University, Guangzhou, 510631, China

    Zhibin Du & Bo Zhou

  2. The Rugjer Bošković Institute, P. O. Box 180, 10002, Zagreb, Croatia

    Nenad Trinajstić

Authors
  1. Zhibin Du
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  2. Bo Zhou
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  3. Nenad Trinajstić
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Correspondence to Bo Zhou.

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Du, Z., Zhou, B. & Trinajstić, N. Minimum sum-connectivity indices of trees and unicyclic graphs of a given matching number. J Math Chem 47, 842–855 (2010). https://doi.org/10.1007/s10910-009-9604-7

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  • DOI: https://doi.org/10.1007/s10910-009-9604-7

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