An extremal problem on group connectivity of graphs

Let A be an Abelian group, n ≥ 3 be an integer, and e x ( n , A ) be the maximum integer such that every n -vertex simple graph with at most e x ( n , A ) edges is not A -connected. In this paper, we study e x ( n , A ) for | A | ≥ 3 and present lower and upper bounds for 3 ≤ | A | ≤ 4 and an upper bound for | A | ≥ 5 .