Edge Connectivity Problems in Telecommunication Networks
If a communication network N with n stations has every station linked with at least [n/2] other stations, then the edge-connectivity of N equals its minimum degree. Also, in general, this limitation is stated to be the best possibility, as was proved by Chartrand in 1966. A more developed notion of edge-connectivity is introduced, which is called k-component order edge connectivity. It is the minimum number of edges required to be removed so that the order of each disconnected component is less than k.
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Boesch, F., Gross, D., Kazmierczak, L., Suhartomo, A. & Suffel, C., Component Order Edge Connectivity-An Introduction, Congressus Numerantium, 178, pp. 7-14, 2006.
Suhartomo, A., Component Order Edge Connectivity: A Vulnerability Parameter for Communication Networks, Doctoral Thesis, Stevens Institute of Technology, Hoboken NJ, May 2007.
Boesch, F., Gross, D., Suffel, C., Saccoman, J.T., Kazmierczak, L.W. & Suhartomo, A., A Generalization of A Theorem of Chartrand, Networks, 2009. doi:10.1002/net.20297.
Plesnik, J. & Znam, S., On Equality of Edge – Connectivity and Minimum Degree of Graph, Archivum Mathematicum (BRNO), 25(1-2), pp. 19-26, 1989.
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