A generalization of dual polar graph of orthogonal space

作者：Guo Jun; Gao Suogang^*

来源：Finite Fields and Their Applications, 2009, 15(6): 661-672.

DOI：10.1016/j.ffa.2009.04.005

• Affine-orthogonal space
• Dual polar graph
• Maximal totally isotropic flat

Let delta = 0, 1 or 2, and let AOG(2 nu delta, F(q)) be the (2 nu delta)-dimensional affine-orthogonal space over a finite field F(q). Define a graph Gamma(delta) whose vertex-set is the set of all maximal totally isotropic flats of AOG(2 nu delta, F(q)), and in which F(1), F(2) are adjacent if and only if dim(F(1) boolean OR F(2)) = nu 1, for any F(1), F(2) is an element of Gamma(delta). First, we show that the distance between any two vertices in Gamma(delta) is determined by means of dimension of their join and prove that Gamma(delta) is a vertex transitive graph with diameter nu inverted right perpendicular(1 delta)/2inverted left perpendicular and valency (q(nu delta) - 1) q(1 delta)[nu 1](q). Next, we show that any maximal clique in Gamma(delta) is isomorphic to the maximal clique Omega(delta)(1) (delta >= 1) with size q(delta) 1, the maximal clique Omega(delta)(2) with size 2q, or the maximal clique Omega(delta)(3) with size q(nu delta) and also compute the total number of maximal cliques in Gamma(delta). Finally, we study the connectivity of some subgraphs of Gamma(delta).

• 出版日期2009-12
• 单位廊坊师范学院; 河北师范大学