On the coefficients of the Laplacian characteristic polynomial of trees

I. Gutman; Ljiljana Pavlović

doi:10.2298/BMAT0328031G

Geodesic

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On the coefficients of the Laplacian characteristic polynomial of trees

I. Gutman ; Ljiljana Pavlović

Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 28 (2003), p. 31 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Résumé

Let the Laplacian characteristic polynomial of an $n$-vertex tree $T$ be of the form $\psi(T,\lambda) = \sum\limits_{k=0}^n (-1)^{n-k}\,c_k(T)\,\lambda^k$ . 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 $c_3(S_n)=c_3(P_n)$ .

Zbl

DOI : 10.2298/BMAT0328031G

Classification : 05C05 05C12 05C50
Keywords: Laplacian spectrum, Laplacian characteristic polynomial, Trees, Distance (in graph), Wiener number

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     title = {On the coefficients of the {Laplacian} characteristic polynomial of trees},
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I. Gutman; Ljiljana Pavlović. On the coefficients of the Laplacian characteristic polynomial of trees. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 28 (2003), p. 31 . doi : 10.2298/BMAT0328031G. http://geodesic.mathdoc.fr/articles/10.2298/BMAT0328031G/

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