The matching energy of graphs with given edge connectivity

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Let G be a simple graph of order n and μ₁,μ₂,,μₙ the roots of its matching polynomial. The matching energy of G is defined as the sum ∑ᵢ₌₁ⁿ|μᵢ|. Let Kₙ₋₁,₁ᵏ be the graph obtained from K₁∪ Kₙ₋₁ by adding k edges between V(K₁) and V(Kₙ₋₁). In this paper, we show that Kₙ₋₁,₁ᵏ has maximum matching energy among all connected graph with order n and edge connectivity k.