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Total domination in the Cartesian product of a graph and $$K_2$$ or $$C_n$$. (English) Zbl 1242.05208
Summary: Let $$G\square H$$ denote the Cartesian product of graphs $$G$$ and $$H$$ and $$\gamma_t(H)$$ denote the total domination number of $$H$$. We characterize all graphs $$H$$ which satisfy $$\gamma_t(K_2\square H)= \gamma_t(H)$$ and $$\gamma_t(C_n)\gamma_t(H)= 2\gamma_t(C_n\square H)$$, respectively.

##### MSC:
 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) 05C76 Graph operations (line graphs, products, etc.)
##### Keywords:
domination; total domination; Cartesian product