A note on an extremal problem for group-connectivity

In Luo et al. (2012), an extremal graph theory problem is proposed for group connectivity: for an abelian group A with | A | ≥ 3 and an integer n ≥ 3 , find e x ( n , A ) , where e x ( n , A ) is the maximum number so that every n -vertex simple graph with at most e x ( n , A ) edges is not A -connected. In this paper, we determine the values e x ( n , A ) for A = Z k where k ≥ 3 is an odd integer and for A = Z 4 , each of which solves some open problem proposed in Luo et al. (2012). Furthermore, the values e x ( n , Z 4 ) also imply a characterization of Z 4 -connected graphic sequences.