On the number of edges of a simple Z ₂ × Z ₂ -connected graph

Abstract

Luo, Xu and Yu proposed an extremal problem on group connectivity of graphs as follows: for an abelian group A with | A | ≥ 3 and an integer n ≥ 3, find ex ( n , A ), where ex ( n , A ) is the maximum number such that every simple graph with n vertices and at most ex ( n , A ) edges is not A -connected. In this paper, we determine the values ex ( n , Z ₂  ×  Z ₂ ) for 3 ≤ n ≤ 10.