Geodesic
On a relationship between the eigenvectors of weighted graphs and their subgraphs
Diskretnaya Matematika, Tome 16 (2004) no. 4, pp. 32-40.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the problem of finding connections between eigen-vectors and subgraphs of a weighted undirected graph $G$. Let $G$ have $n$ vertices labelled $1,\ldots,n$, $\lambda$ be an eigen-value of the graph $G$ of multiplicity $t\ge 1$, and let $X^{(i)}=(x_1^{(i)},\ldots,x_n^{(i)})$, $i=1,\ldots,t$, be linearly independent eigen-vectors corresponding to this eigen-value. We obtain formulas representing the components $x_j^{(i)}$ of the eigen-vectors $X^{(i)}$ in terms of some characteristics of special subgraphs of the graph $G$, $i=1,\ldots,t$, $j=1,\ldots,n$. An illustrative example is given. 
@article{DM_2004_16_4_a3,
     author = {M. I. Skvortsova and I. V. Stankevich},
     title = {On a relationship between the eigenvectors of weighted graphs and their subgraphs},
     journal = {Diskretnaya Matematika},
     pages = {32--40},
     publisher = {mathdoc},
     volume = {16},
     number = {4},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2004_16_4_a3/}
}
TY  - JOUR
AU  - M. I. Skvortsova
AU  - I. V. Stankevich
TI  - On a relationship between the eigenvectors of weighted graphs and their subgraphs
JO  - Diskretnaya Matematika
PY  - 2004
SP  - 32
EP  - 40
VL  - 16
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2004_16_4_a3/
LA  - ru
ID  - DM_2004_16_4_a3
ER  - 
%0 Journal Article
%A M. I. Skvortsova
%A I. V. Stankevich
%T On a relationship between the eigenvectors of weighted graphs and their subgraphs
%J Diskretnaya Matematika
%D 2004
%P 32-40
%V 16
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2004_16_4_a3/
%G ru
%F DM_2004_16_4_a3
M. I. Skvortsova; I. V. Stankevich. On a relationship between the eigenvectors of weighted graphs and their subgraphs. Diskretnaya Matematika, Tome 16 (2004) no. 4, pp. 32-40. http://geodesic.mathdoc.fr/item/DM_2004_16_4_a3/

[1] Tsvetkovich D., Dub M., Zakhs Kh., Spektry grafov. Teoriya i primenenie, Naukova dumka, Kiev, 1984 | MR

[2] Trinajstic N., “The characteristic polynomial of a chemical graph”, Math. Chem., 2:3 (1988), 197–215 | DOI | MR