Geodesic
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 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Voir la notice de l'article

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 $c_3(S_n)=c_3(P_n)$ .
DOI : 10.2298/BMAT0328031G
Classification : 05C05 05C12 05C50
Keywords: Laplacian spectrum, Laplacian characteristic polynomial, Trees, Distance (in graph), Wiener number 
@article{10_2298_BMAT0328031G,
     author = {I. Gutman and Ljiljana Pavlovi\'c},
     title = {On the coefficients of the {Laplacian} characteristic polynomial of trees},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {31 },
     year = {2003},
     volume = {28},
     doi = {10.2298/BMAT0328031G},
     zbl = {1080.05519},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/BMAT0328031G/}
}
TY  - JOUR
AU  - I. Gutman
AU  - Ljiljana Pavlović
TI  - On the coefficients of the Laplacian characteristic polynomial of trees
JO  - Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles
PY  - 2003
SP  - 31 
VL  - 28
UR  - http://geodesic.mathdoc.fr/articles/10.2298/BMAT0328031G/
DO  - 10.2298/BMAT0328031G
LA  - en
ID  - 10_2298_BMAT0328031G
ER  - 
%0 Journal Article
%A I. Gutman
%A Ljiljana Pavlović
%T On the coefficients of the Laplacian characteristic polynomial of trees
%J Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles
%D 2003
%P 31 
%V 28
%U http://geodesic.mathdoc.fr/articles/10.2298/BMAT0328031G/
%R 10.2298/BMAT0328031G
%G en
%F 10_2298_BMAT0328031G
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

Cité par Sources :