On some locally 3-transposition graphs
Let ∑_n^ε be the graph defined on the (+)- points of an n-dimensional GF(3)-space carrying a nondegenerate symmetric bilinear form with discriminant ε, points are adjacent if they are perpendicular. We prove that if ε = 1, n ≥ 6 (resp.ε=-1,n≥7) then ∑_(n+1)^εis the unique connected locally ∑_n^ε gra...
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
2011
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| Online Access: | https://hdl.handle.net/10356/97315 http://hdl.handle.net/10220/6955 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | Let ∑_n^ε be the graph defined on the (+)- points of an n-dimensional GF(3)-space carrying a nondegenerate symmetric bilinear form with discriminant ε, points are adjacent if they are perpendicular. We prove that if ε = 1, n ≥ 6 (resp.ε=-1,n≥7) then ∑_(n+1)^εis the unique connected locally ∑_n^ε graph. One may view this result as a characterization of a class of c^k. C_2-geometries (or 3-transposition groups). We briefly discuss an application of the result to a characterization of Fischer's sporadic groups. |
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