On the total {k}-domination number of Cartesian products of graphs |
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| Authors: | Ning Li Xinmin Hou |
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| Institution: | (1) Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, China |
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| Abstract: | Let γ
t
{k}(G) denote the total {k}-domination number of graph G, and let
denote the Cartesian product of graphs G and H. In this paper, we show that for any graphs G and H without isolated vertices,
. As a corollary of this result, we have
for all graphs G and H without isolated vertices, which is given by Pak Tung Ho (Util. Math., 2008, to appear) and first appeared as a conjecture proposed by Henning and Rall (Graph. Comb. 21:63–69, 2005).
The work was supported by NNSF of China (No. 10701068 and No. 10671191). |
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| Keywords: | Total {k}-domination Total domination Cartesian product |
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