×

zbMATH — the first resource for mathematics

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.)
PDF BibTeX XML Cite