Stability of cartesian products |
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| Authors: | Julie Sims DA Holton |
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| Institution: | 1. University of Melbourne, Parkville, Victoria, Australia 3052;2. University of Aberdeen UK |
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| Abstract: | We complete the work started by Holton and Grant concerning the semi-stability of non-trivial connected cartesian products and show that all such products are semi-stable. Further we show that except for certain (listed) restricted graphs, connected cartesian products are semi-stable at every vertex. Finally, we show that the cartesian product of any two graphs is not semi-stable if and only if one of them is totally disconnected and the other is not semi-stable. |
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