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Science in China Series A: Mathematics

, Volume 52, Issue 2, pp 361–380 | Cite as

Orthogonal graphs of characteristic 2 and their automorphisms

  • ZheXian Wan
  • Kai ZhouEmail author
Article

Abstract

The (singular) orthogonal graph O(2ν + δ, q) over a field with q elements and of characteristic 2 (where ν ⩾ 1, and δ = 0, 1 or 2) is introduced. When ν = 1, O(2 · 1, q), O(2 · 1 + 1, q) and O(2 · 1 + 2, q) are complete graphs with 2, q + 1 and q 2 + 1 vertices, respectively. When ν ⩾ 2, O(2ν + δ, q) is strongly regular and its parameters are computed. O(2ν + 1, q) is isomorphic to the symplectic graph Sp(2ν, q). The chromatic number of O(2ν + ν, q) except when δ = 0 and ν is odd is computed and the group of graph automorphisms of O(2ν + δ, q) is determined.

Keywords

singular orthogonal graphs regularity chromatic number automorphisms 

MSC(2000)

05E15 05E30 

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Copyright information

© Science in China Press and Springer-Verlag GmbH 2009

Authors and Affiliations

  1. 1.Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina

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