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

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