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arXiv · 1512.01333

Laplacian Coefficient, Matching Polynomial and Incidence Energy of of Trees with Described Maximum Degree

Ya-Lei Jin·Yeong-Nan Yeh·Xiao-Dong Zhang
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Abstract

Let $\mathcal{L}(T,λ)=\sum_{k=0}^n(-1)^{k}c_{k}(T)λ^{n-k}$ be the characteristic polynomial of its Laplacian matrix of a tree $T$. This paper studied some properties of the generating function of the coefficients sequence $(c_0, \cdots, c_n)$ which are related with the matching polynomials of division tree of $T$. These results, in turn, are used to characterize all extremal trees having the minimum Laplacian coefficient generation function and the minimum incidence energy of trees with described maximum degree, respectively.

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Ya-Lei Jin, Yeong-Nan Yeh, Xiao-Dong Zhang. 2015-12-04. Laplacian Coefficient, Matching Polynomial and Incidence Energy of of Trees with Described Maximum Degree. https://arxiv.org/abs/1512.01333

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