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This article is cited in 6 scientific papers (total in 6 papers)
On stable and unstable trees
V. A. Kolmykov
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
Citation:
V. A. Kolmykov, “On stable and unstable trees”, Diskr. Mat., 17:2 (2005), 150–152; Discrete Math. Appl., 15:2 (2005), 207–209
Linking options:
https://www.mathnet.ru/eng/dm107https://doi.org/10.4213/dm107 https://www.mathnet.ru/eng/dm/v17/i2/p150
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Abstract page: | 591 | Full-text PDF : | 242 | References: | 58 | First page: | 1 |
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