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On the signed edge domination number of graphs |
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| Authors: | S Akbari S Bolouki |
| Institution: | a Institute for Studies in Theoretical Physics and Mathematics, P.O. Box 19395-5746, Tehran, Iran b Department of Mathematical Sciences, Sharif University of Technology, P.O. Box 11365-9415, Tehran, Iran c Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran |
| Abstract: | Let  be the signed edge domination number of G. In 2006, Xu conjectured that: for any 2-connected graph G of order n(n≥2),  . 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  . Also for every two natural numbers m and n, we determine  , where Km,n is the complete bipartite graph with part sizes m and n. |
| Keywords: | Signed edge domination number _method=retrieve& _eid=1-s2 0-S0012365X08005268& _mathId=si18 gif& _pii=S0012365X08005268& _issn=0012365X& _acct=C000051805& _version=1& _userid=1154080& md5=f63cd9797c4123d01aac089104661161')" style="cursor:pointer m-connected" target="_blank">" alt="Click to view the MathML source" title="Click to view the MathML source">m-connected Complete bipartite graph |
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