Bulletin

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Volume 37 • Number 4 • 2014

• 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

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