Unitary inner product graphs and their automorphisms.

Let q 2 be a finite field of order q 2 and 2 ν + δ ≥ 2 be an integer with δ = 0 or 1 , where q is a power of a prime. We introduce the concept of the unitary inner product graph U i (2 ν + δ , q 2) over q 2 and determine its automorphism group. We obtain two necessary and sufficient conditions for two vertices of U i (2 ν + δ , q 2) and two edges of U i (2 ν + δ , q 2) , respectively, are in the same orbit under the action of the automorphism group of U i (2 ν + δ , q 2). [ABSTRACT FROM AUTHOR]