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 AA with |A|≥3|A|≥3 and an integer n≥3n≥3, find ex(n,A)ex(n,A), where ex(n,A)ex(n,A) is the maximum number so that every nn-vertex simple graph with at most ex(n,A)ex(n,A) edges is not AA-connected. In this paper, we determine the values ex(n,A)ex(n,A) for A=ZkA=Zk where k≥3k≥3 is an odd integer and for A=Z4A=Z4, each of which solves some open problem proposed in Luo et al. (2012). Furthermore, the values ex(n,Z4)ex(n,Z4) also imply a characterization of Z4Z4-connected graphic sequences.