Orthogonal graphs of characteristic 2 and their automorphisms
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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.
Keywordssingular orthogonal graphs regularity chromatic number automorphisms
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- 1.Wan Z. Geometry of Classical Groups over Finite Fields, 2nd ed. Beijing-New York: Science Press, 2002Google Scholar
- 3.Godsil C, Royle G. Algebraic Graph Theory. Graduate Texts in Mathematics, Vol. 207. New York: Springer-Verlag, 2001Google Scholar
- 4.Hoffman A J. On eigenvalues and colorings of graphs. In: Graph Theory and its Applications. New York: Academic Press, 1970Google Scholar