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Let $\gamma\prime_{s}(G)$ be the signed edge domination number of G. In 2006, Xu conjectured that: for any 2-connected graph G of order $n(n \geq 2), \gamma\prime_{s}(G)\geq 1$. In this article we show that this conjecture is not true. More precisely, we show that for any positive integer $m$, there exists an $m$-connected graph $G$ such that $\gamma\prime_{s}(G) \leq -\frac{m}{6}|V(G)| $. Also for every two natural numbers $m$ and $n$, we determine $\gamma\prime_{s}(K_{m,n})$, where $K_{m,n}$ is the complete bipartite graph with part sizes $m$ and $n$.
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