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On the Laplacian Coefficients of Tricyclic Graphs with Prescribed Matching Number

Jing LuoZhongxun ZhuRunze Wan — 2017

Discussiones Mathematicae Graph Theory

Let [...] φ(L(G))=det (xI−L(G))=∑k=0n(−1)kck(G)xn−k φ ( L ( G ) ) = det ( x I - L ( G ) ) = 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 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).

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