Abstract
Let G be a connected graph. The Szeged index of G is defined as \(Sz(G)=\sum \nolimits _{e=uv\in E(G)}n_{u}(e|G)n_{v}(e|G)\), where \(n_{u}(e|G)\) (resp., \(n_{v}(e|G)\)) is the number of vertices whose distance to vertex u (resp., v) is smaller than the distance to vertex v (resp., u), and \(n_{0}(e|G)\) is the number of vertices equidistant from both ends of e. Let \(\mathcal {M}(2\beta )\) be the set of unicyclic graphs with order \(2\beta \) and a perfect matching. In this paper, we determine the minimum value of Szeged index and characterize the extremal graph with the minimum Szeged index among all unicyclic graphs with perfect matchings.
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This paper supported by program for excellent talents in Hunan Normal University (ET13101).
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Liu, H., Deng, H. & Tang, Z. Minimum Szeged index among unicyclic graphs with perfect matchings. J Comb Optim 38, 443–455 (2019). https://doi.org/10.1007/s10878-019-00390-5
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DOI: https://doi.org/10.1007/s10878-019-00390-5