An extremal problem on group connectivity of graphs

Abstract

Let A be an Abelian group, n≥ 3 be an integer, and ex(n, A) be the maximum integer such that every n-vertex simple graph with at most ex(n, A) edges is not A-connected. In this paper, we study ex(n, A) for {pipe}. A{pipe} ≥ 3 and present lower and upper bounds for 3 ≤ {pipe}. A{pipe} ≤ 4 and an upper bound for {pipe}. A{pipe} ≥ 5. © 2012 Elsevier Ltd.