A local characterization of the graphs of alternating forms and the graphs of quadratic forms over GF(2)
Let Δ be the line graph of PG(n –1,2), Alt(n,2) be the graph of the n-dimensional alternating forms over GF(2), n ≥ 4. Let Γ be a connected locally Δ graph such that 1. the number of common neighbours of any pair of vertices at distance two is the same as in Alt(n,2). 2. the valency of the subgraph...
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| Format: | Conference Paper |
| Language: | English |
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2011
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| Online Access: | https://hdl.handle.net/10356/91646 http://hdl.handle.net/10220/6956 |
| _version_ | 1811682964134690816 |
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| author | Munemasa, A. Pasechnik, Dmitrii V. Shpectorov, Sergey V. |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Munemasa, A. Pasechnik, Dmitrii V. Shpectorov, Sergey V. |
| author_sort | Munemasa, A. |
| collection | NTU |
| description | Let Δ be the line graph of PG(n –1,2), Alt(n,2) be the graph of the n-dimensional alternating forms over GF(2), n ≥ 4. Let Γ be a connected locally Δ graph such that 1. the number of common neighbours of any pair of vertices at distance two is the same as in Alt(n,2). 2. the valency of the subgraph induced on the second neighbourhood of any vertex is the same as in Alt(n,2). It is shown that Γ is covered either by Alt(n,2) or by the graph of (n – l)-dimensional GF(2)-quadratic forms Quad(n – 1,2). |
| first_indexed | 2024-10-01T04:05:12Z |
| format | Conference Paper |
| id | ntu-10356/91646 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T04:05:12Z |
| publishDate | 2011 |
| record_format | dspace |
| spelling | ntu-10356/916462023-02-28T19:17:23Z A local characterization of the graphs of alternating forms and the graphs of quadratic forms over GF(2) Munemasa, A. Pasechnik, Dmitrii V. Shpectorov, Sergey V. School of Physical and Mathematical Sciences Finite Geometry and Combinatorics (2nd : 1993 : Deinze, Belgian) DRNTU::Science::Mathematics::Number theory Let Δ be the line graph of PG(n –1,2), Alt(n,2) be the graph of the n-dimensional alternating forms over GF(2), n ≥ 4. Let Γ be a connected locally Δ graph such that 1. the number of common neighbours of any pair of vertices at distance two is the same as in Alt(n,2). 2. the valency of the subgraph induced on the second neighbourhood of any vertex is the same as in Alt(n,2). It is shown that Γ is covered either by Alt(n,2) or by the graph of (n – l)-dimensional GF(2)-quadratic forms Quad(n – 1,2). Published version 2011-08-11T03:10:49Z 2019-12-06T18:09:30Z 2011-08-11T03:10:49Z 2019-12-06T18:09:30Z 1993 1993 Conference Paper Munemasa , A., Pasechnik, D. V., & Shpectorov, S. V. (1993). A local characterization of the graphs of alternating forms and the graphs of quadratic forms over GF(2). The Second International Conference at Deinze, pp. 303-317. https://hdl.handle.net/10356/91646 http://hdl.handle.net/10220/6956 10.1017/CBO9780511526336.029 en © 1993 Cambridge University Press. This paper was published in Finite geometry and combinatorics and is made available as an electronic reprint (preprint) with permission of Cambridge University Press. The paper can be found at the following DOI: http://dx.doi.org/10.1017/CBO9780511526336.029. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law. application/pdf |
| spellingShingle | DRNTU::Science::Mathematics::Number theory Munemasa, A. Pasechnik, Dmitrii V. Shpectorov, Sergey V. A local characterization of the graphs of alternating forms and the graphs of quadratic forms over GF(2) |
| title | A local characterization of the graphs of alternating forms and the graphs of quadratic forms over GF(2) |
| title_full | A local characterization of the graphs of alternating forms and the graphs of quadratic forms over GF(2) |
| title_fullStr | A local characterization of the graphs of alternating forms and the graphs of quadratic forms over GF(2) |
| title_full_unstemmed | A local characterization of the graphs of alternating forms and the graphs of quadratic forms over GF(2) |
| title_short | A local characterization of the graphs of alternating forms and the graphs of quadratic forms over GF(2) |
| title_sort | local characterization of the graphs of alternating forms and the graphs of quadratic forms over gf 2 |
| topic | DRNTU::Science::Mathematics::Number theory |
| url | https://hdl.handle.net/10356/91646 http://hdl.handle.net/10220/6956 |
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