A local characterization of the graphs of alternating forms and the graphs of quadratic forms over GF(2)

• Main Authors: Munemasa, A., Pasechnik, Dmitrii V., Shpectorov, Sergey V.
• Other Authors: School of Physical and Mathematical Sciences
• Format: Conference or Workshop Item
• Language: English
• Published: 2011
• Subjects: DRNTU::Science::Mathematics::Number theory
• Online Access: https://hdl.handle.net/10356/91646; http://hdl.handle.net/10220/6956
• Institution: Nanyang Technological University

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).