the disc structures of a4-graph for particular untwisted groups

Let t be an elements of order 3 in a finite simple group g. let x = t g be a conjugacy class of t in g. the a4-graph, represented as a4(g, x), is a simple graph has x as a vertex set and two vertices x, y ∈ x, joined by edge whenever x ≠ y and xy^−1 = yx^−1. in this paper, we investigate the discs structure and determine the clique number, girth and diameter of a4(g, x) when g is isomorphic to one of the untwisted groups g2(2)′, g2(3) or g2(4).