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Diskretnaya Matematika, 2005, Volume 17, Issue 2, Pages 150–152
DOI: https://doi.org/10.4213/dm107
(Mi dm107)
 

This article is cited in 6 scientific papers (total in 6 papers)

On stable and unstable trees

V. A. Kolmykov
Full-text PDF (334 kB) Citations (6)
References:
Abstract: A graph is called stable if the adjacency matrix of the graph is nonsingular and unstable otherwise. Such terminology is related to applications in chemistry. We consider weighted graphs, this generalisation is also justified from the point of view of applications in chemistry, since it removes some restrictions in the Huckel model. Stability and instability of a weighted tree do not depend on replacements of any non-zero weights by arbitrary non-zero weights, that is, under replacement of ones in the adjacency matrix of a tree by arbitrary non-zero numbers singularity or non-singularity survives. We suggest a characterisation of stable and unstable trees which is based on a construction of trees from the so-called elementary trees.
Received: 31.07.2000
English version:
Discrete Mathematics and Applications, 2005, Volume 15, Issue 2, Pages 207–209
DOI: https://doi.org/10.1515/1569392053971488
Bibliographic databases:
UDC: 519.172
Language: Russian
Citation: V. A. Kolmykov, “On stable and unstable trees”, Diskr. Mat., 17:2 (2005), 150–152; Discrete Math. Appl., 15:2 (2005), 207–209
Citation in format AMSBIB
\Bibitem{Kol05}
\by V.~A.~Kolmykov
\paper On stable and unstable trees
\jour Diskr. Mat.
\yr 2005
\vol 17
\issue 2
\pages 150--152
\mathnet{http://mi.mathnet.ru/dm107}
\crossref{https://doi.org/10.4213/dm107}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2167809}
\zmath{https://zbmath.org/?q=an:1102.05017}
\elib{https://elibrary.ru/item.asp?id=9135432}
\transl
\jour Discrete Math. Appl.
\yr 2005
\vol 15
\issue 2
\pages 207--209
\crossref{https://doi.org/10.1515/1569392053971488}
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  • https://www.mathnet.ru/eng/dm107
  • https://doi.org/10.4213/dm107
  • https://www.mathnet.ru/eng/dm/v17/i2/p150
  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Дискретная математика
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    Abstract page:591
    Full-text PDF :242
    References:58
    First page:1
     
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