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| Paper IPM / M / 8859 |
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| Abstract: | |
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Let γ′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 ≥ 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 m-connected graph G such that γ′s(G) ≤ −[(m)/6]|V(G)| . Also for every two natural numbers m and n, we determine γ′s(Km,n), where Km,n is the complete bipartite graph with part sizes m and n.
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