Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiques Vol. CXXVII, No. 28, pp. 31–40 (2003) 

On the coefficients of the Laplacian characteristic polynomial of treesI. Gutman and Ljiljana PavlovicIFaculty of Science, University of Kragujevac, P. O. Box 60, 34000 Kragujevac, Serbia and MontenegroAbstract: Let the Laplacian characteristic polynomial of an $n$vertex tree $T$ be of the form $\psi(T,\lambda) = \sum\limits_{k=0}^n (1)^{nk} c_k(T) \lambda^k$ . Then, as well known, $c_0(T)=0$ and $c_1(T)=n$ . If $T$ differs from the star ($S_n$) and the path ($P_n$), which requires $n \geq 5$ , then $c_2(S_n) < c_2(T) < c_2(P_n)$ and $c_3(S_n) < c_3(T) < c_3(P_n)$ . If $n=4$ , then $c_3(S_n)=c_3(P_n)$ . Keywords: Laplacian spectrum, Laplacian characteristic polynomial, Trees, Distance (in graph), Wiener number Classification (MSC2000): 05C05, 05C12, 05C50 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 17 Sep 2003. This page was last modified: 20 Jun 2011.
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