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) no. 1
Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts
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 $c_3(S_n)=c_3(P_n)$ .
Keywords:
Laplacian spectrum, Laplacian characteristic polynomial, Trees, Distance (in graph), Wiener number
@article{BASS_2003_28_1_a3,
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 - 40},
year = {2003},
volume = {28},
number = {1},
zbl = {1080.05519},
url = {http://geodesic.mathdoc.fr/item/BASS_2003_28_1_a3/}
}
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 EP - 40 VL - 28 IS - 1 UR - http://geodesic.mathdoc.fr/item/BASS_2003_28_1_a3/ ID - BASS_2003_28_1_a3 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 - 40 %V 28 %N 1 %U http://geodesic.mathdoc.fr/item/BASS_2003_28_1_a3/ %F BASS_2003_28_1_a3
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) no. 1. http://geodesic.mathdoc.fr/item/BASS_2003_28_1_a3/