Geodesic
On the Laplacian Coefficients of Tricyclic Graphs with Prescribed Matching Number
Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 3, pp. 505-522

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Let ϕ (L(G)) = det(x I−L(G)) = Σ_k=0^n (−1)^k c_k (G) x^n−k be the Laplacian characteristic polynomial of G. In this paper, we characterize the minimal graphs with the minimum Laplacian coefficients in 𝒢_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 𝒢_n,n+2 (i).
Keywords: Laplacian characteristic polynomial, Laplacian-like energy, tricyclic graph 
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Luo, Jing; Zhu, Zhongxun; Wan, Runze. On the Laplacian Coefficients of Tricyclic Graphs with Prescribed Matching Number. Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 3, pp. 505-522. http://geodesic.mathdoc.fr/item/DMGT_2017_37_3_a0/