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On the total domination number of cross products of graphs |
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| Authors: | Mohamed El-Zahar Antoaneta Klobucar |
| Institution: | a Department of Mathematics, Faculty of Science, Ain Shams University, Abbaseia, Cairo, Egypt b CNRS, GeoD Research Group, ERTé Maths à modeler, Institut Fourier, 100 rue des maths, 38402 Saint Martin d’Hères Cedex, France c Ekonomski Facultet, Osijek, Croatia |
| Abstract: | We give lower and upper bounds on the total domination number of the cross product of two graphs, γt(G×H). These bounds are in terms of the total domination number and the maximum degree of the factors and are best possible. We further investigate cross products involving paths and cycles. We determine the exact values of γt(G×Pn) and γt(Cn×Cm) where Pn and Cn denote, respectively, a path and a cycle of length n. |
| Keywords: | Total domination number |
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