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Let [...] φ(L(G))=det (xI−L(G))=∑k=0n(−1)kck(G)xn−k $\phi \left(L\left(G\right)\right)=det(xI-L\left(G\right))={\sum }_{k=0}^n{(-1)}^k{c}_k\left(G\right)x^{n-k}$ be the Laplacian characteristic polynomial of G. In this paper, we characterize the minimal graphs with the minimum Laplacian coefficients in n,n+2(i) (the set of all tricyclic graphs with fixed order n and matching number i). Furthermore, the graphs with the minimal Laplacian-like energy, which is the sum of square roots of all roots on ϕ(L(G)), is also determined in n,n+2(i).