Automorphism groups of the PSL 2 (𝑞) commuting involution graphs

Key Points

• The aim is to determine the automorphism group of the commuting involution graph associated with the group PSL 2(q).
• Defined the commuting involution graph for a group G and a conjugacy class of involutions X.
• Analyzed the adjacency condition for vertices in the graph.
• Investigated the properties of PSL 2(q) to determine the structure of the automorphism group.
• The automorphism group of the graph is fully characterized for G = PSL 2(q).
• Key properties of involutions and their commutativity were utilized to clarify the automorphism structure.