Algorithms computing O(n, Z)-orbits of P-critical edge-bipartite graphs and P-critical unit forms using Maple and C#
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...
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| Дата: | 2013 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут прикладної математики і механіки НАН України
2013
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/152352 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1523522019-06-12T01:25:18Z Algorithms computing O(n, Z)-orbits of P-critical edge-bipartite graphs and P-critical unit forms using Maple and C# Polak, A. Simson, D. 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. 2013 Article 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 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Polak, A. Simson, D. |
| spellingShingle |
Polak, A. Simson, D. Algorithms computing O(n, Z)-orbits of P-critical edge-bipartite graphs and P-critical unit forms using Maple and C# Algebra and Discrete Mathematics |
| author_facet |
Polak, A. Simson, D. |
| author_sort |
Polak, A. |
| title |
Algorithms computing O(n, Z)-orbits of P-critical edge-bipartite graphs and P-critical unit forms using Maple and C# |
| title_short |
Algorithms computing O(n, Z)-orbits of P-critical edge-bipartite graphs and P-critical unit forms using Maple and C# |
| title_full |
Algorithms computing O(n, Z)-orbits of P-critical edge-bipartite graphs and P-critical unit forms using Maple and C# |
| title_fullStr |
Algorithms computing O(n, Z)-orbits of P-critical edge-bipartite graphs and P-critical unit forms using Maple and C# |
| title_full_unstemmed |
Algorithms computing O(n, Z)-orbits of P-critical edge-bipartite graphs and P-critical unit forms using Maple and C# |
| title_sort |
algorithms computing o(n, z)-orbits of p-critical edge-bipartite graphs and p-critical unit forms using maple and c# |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/152352 |
| citation_txt |
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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT polaka algorithmscomputingonzorbitsofpcriticaledgebipartitegraphsandpcriticalunitformsusingmapleandc AT simsond algorithmscomputingonzorbitsofpcriticaledgebipartitegraphsandpcriticalunitformsusingmapleandc |
| first_indexed |
2023-05-20T17:38:07Z |
| last_indexed |
2023-05-20T17:38:07Z |
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1796153740794789888 |