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Diskretnaya Matematika, 2004, Volume 16, Issue 4, Pages 32–40
DOI: https://doi.org/10.4213/dm173
(Mi dm173)
 

On a relationship between the eigenvectors of weighted graphs and their subgraphs

M. I. Skvortsova, I. V. Stankevich
References:
Abstract: 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.
Received: 23.01.2003
English version:
Discrete Mathematics and Applications, 2004, Volume 14, Issue 6, Pages 569–577
DOI: https://doi.org/10.1515/1569392043272502
Bibliographic databases:
UDC: 519.17
Language: Russian
Citation: M. I. Skvortsova, I. V. Stankevich, “On a relationship between the eigenvectors of weighted graphs and their subgraphs”, Diskr. Mat., 16:4 (2004), 32–40; Discrete Math. Appl., 14:6 (2004), 569–577
Citation in format AMSBIB
\Bibitem{SkvSta04}
\by M.~I.~Skvortsova, I.~V.~Stankevich
\paper On a relationship between the eigenvectors of weighted graphs and their subgraphs
\jour Diskr. Mat.
\yr 2004
\vol 16
\issue 4
\pages 32--40
\mathnet{http://mi.mathnet.ru/dm173}
\crossref{https://doi.org/10.4213/dm173}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2141143}
\zmath{https://zbmath.org/?q=an:1104.05049}
\transl
\jour Discrete Math. Appl.
\yr 2004
\vol 14
\issue 6
\pages 569--577
\crossref{https://doi.org/10.1515/1569392043272502}
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  • https://www.mathnet.ru/eng/dm/v16/i4/p32
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