Minimum Szeged index among unicyclic graphs with perfect matchings

Hechao Liu, Hanyuan Deng and Zikai Tang ()
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Hechao Liu: Hunan Normal University
Hanyuan Deng: Hunan Normal University
Zikai Tang: Hunan Normal University

Journal of Combinatorial Optimization, 2019, vol. 38, issue 2, No 7, 443-455

Abstract: Abstract Let G be a connected graph. The Szeged index of G is defined as $$Sz(G)=\sum \nolimits _{e=uv\in E(G)}n_{u}(e|G)n_{v}(e|G)$$ S z ( G ) = ∑ e = u v ∈ E ( G ) n u ( e | G ) n v ( e | G ) , where $$n_{u}(e|G)$$ n u ( e | G ) (resp., $$n_{v}(e|G)$$ 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 $$n_{0}(e|G)$$ n 0 ( e | G ) is the number of vertices equidistant from both ends of e. Let $$\mathcal {M}(2\beta )$$ M ( 2 β ) be the set of unicyclic graphs with order $$2\beta $$ 2 β 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.

Keywords: Szeged index; Unicyclic graphs; Perfect matching (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10878-019-00390-5

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