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28 March 2024
 
  » arxiv » 1512.1333

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Laplacian Coefficient, Matching Polynomial and Incidence Energy of of Trees with Described Maximum Degree
Ya-Lei Jin ; Yeong-Nan Yeh ; Xiao-Dong Zhang ;
Date 4 Dec 2015
AbstractLet $mathcal{L}(T,lambda)=sum_{k=0}^n(-1)^{k}c_{k}(T)lambda^{n-k}$ 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.
Source arXiv, 1512.1333
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