On an open problem concerning total domination critical graphs |
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Authors: | Doost Ali Mojdeh Nader Jafari Rad |
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Institution: | 1. Department of Mathematics, University of Mazandaran, P.O. Box 47416-1467, Babolsar, Iran;2. Institute for Studies in Theoretical Physics and Mathematics (IPM), Tehran, Iran |
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Abstract: | A graph G with no isolated vertex is total domination vertex critical if for any vertex v of G that is not adjacent to a vertex of degree one, the total domination number of G-v is less than the total domination number of G . We call these graphs γt-critical. If such a graph G has total domination number k, we call it k -γt-critical. We verify an open problem of k -γt-critical graphs and obtain some results on the characterization of total domination critical graphs of order n=Δ(G)(γt(G)-1)+1. |
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Keywords: | primary 05C69 secondary 05C70 |
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