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| Volume 37 • Number 4 • 2014 |
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A Sufficient Condition on Group Connectivity of Graphs
Qiaoling Ma
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 obtain a necessary condition for a graph being $A$-connected. Employing the condition we present a lower bound for $ex$$($n$,$Z3$)$ which improves some known result and prove that every cubic graph (not necessarily simple graph) with order at least 18 is not $Z$3-connected.
2010 Mathematics Subject Classification: 05C21
Full text: PDF
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