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Paper IPM / M / 8859  


Abstract:  
Let γ′_{s}(G) be the signed edge domination number of G. In 2006, Xu conjectured that: for any 2connected graph G of order n(n ≥ 2), γ′_{s}(G) ≥ 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 mconnected graph G such that γ′_{s}(G) ≤ −[(m)/6]V(G) . Also for every two natural numbers m and n, we determine γ′_{s}(K_{m,n}), where K_{m,n} is the complete bipartite graph with part sizes m and n.
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