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On the total domatic number of regular graphs
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نویسنده
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Aram H. ,Sheikholeslami S. M. ,Volkmann L.
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منبع
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transactions on combinatorics - 2012 - دوره : 1 - شماره : 1 - صفحه:45 -51
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چکیده
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A set s of vertices of a graph g = (v;e) without isolated vertex is a total dominating set if every vertex of v (g) is adjacent to some vertex in s. the total domatic number of a graph g is the maximum number of total dominating sets into which the vertex set of g can be partitioned. we show that the total domatic number of a random r-regular graph is almost surely at most r - 1, and that for 3-regular random graphs, the total domatic number is almost surely equal to 2. we also give a lower bound on the total domatic number of a graph in terms of order, minimum degree and maximum degree. as a corollary, we obtain the result that the total domatic number of an r-regular graph is at least r leg (3 ln(r))
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کلیدواژه
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total dominating set; total domination number; total domatic number; regular graph
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آدرس
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kharazmi university (university of tarbiat moallem), Department of Mathematics, ایران, kharazmi university (university of tarbiat moallem), Department of Mathematics, ایران, RWTH-Aachen University, Lehrstuhl II fur Mathematik, Germany
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پست الکترونیکی
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volkm@math2.rwth-aachen.de
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Authors
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