Orthogonal graphs of characteristic 2 and their automorphisms

【摘要】 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 q2 + 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 + δ,q) except when δ = 0 and ν is odd is computed and the group of graph automorphisms of O(2ν + δ,q) is determined.更多还原

【Abstract】 The (singular) orthogonal graph O(2ν + δ,q) over a field with q elements and of char- acteristic 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 q2 + 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 + δ,q) except when δ = 0 and ν is odd is computed and the group of graph automorphisms of O(2ν + δ,q) is determined.更多还原