Algorithms computing O(n, Z)-orbits of P-critical edge-bipartite graphs and P-critical unit forms using Maple and C#
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Algorithms computing O(n, Z)-orbits of P-critical edge-bipartite graphs and P-critical unit forms using Maple and C#
|
|
| Creator |
Polak, A.
Simson, D. |
|
| Description |
We present combinatorial algorithms constructing loop-free P-critical edge-bipartite (signed) graphs Δ′, with n ≥ 3 vertices, from pairs (Δ, w), with Δ a positive edge-bipartite graph having n-1 vertices and w a sincere root of Δ, up to an action ∗ : UBigrn × O(n, Z) → UBigrn of the orthogonal group O(n, Z) on the set UBigrn of loop-free edge-bipartite graphs, with n ≥ 3 vertices. Here Z is the ring of integers. We also present a package of algorithms for a Coxeter spectral analysis of graphs in UBigrn and for computing the O(n, Z)-orbits of P-critical graphs Δ in UBigrn as well as the positive ones. By applying the package, symbolic computations in Maple and numerical computations in C#, we compute P-critical graphs in UBigrn and connected positive graphs in UBigrn, together with their Coxeter polynomials, reduced Coxeter numbers, and the O(n, Z)-orbits, for n ≤ 10. The computational results are presented in tables of Section 5.
|
|
| Date |
2019-06-10T11:09:15Z
2019-06-10T11:09:15Z 2013 |
|
| Type |
Article
|
|
| Identifier |
Algorithms computing O(n, Z)-orbits of P-critical edge-bipartite graphs and
P-critical unit forms using Maple and C# / A. Polak, D. Simson // Algebra and Discrete Mathematics. — 2013. — Vol. 16, № 2. — С. 242–286. — Бібліогр.: 43 назв. — англ.
1726-3255 2010 MSC:15A63, 11Y16, 68W30, 05E10 16G20, 20B40, 15A21. http://dspace.nbuv.gov.ua/handle/123456789/152352 |
|
| Language |
en
|
|
| Relation |
Algebra and Discrete Mathematics
|
|
| Publisher |
Інститут прикладної математики і механіки НАН України
|
|