An extremal problem on group connectivity of graphs

Authors:
Rong Luo;Rui Xu;Gexin Yu
Affiliations:
School of Mathematical Sciences, Xuzhou Normal University, Xuzhou, Jiangsu, 221116, China and Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, TN 37132, USA;Department of Mathematics, University of West Georgia, Carrollton, GA 30118, USA;Department of Mathematics, College of William and Mary, Williamsburg, VA 23185, USA
Venue:
European Journal of Combinatorics
Year:
2012

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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 |A|=3 and present lower and upper bounds for 3@?|A|@?4 and an upper bound for |A|=5.