Discussiones Mathematicae Graph Theory 32(4) (2012)
629-641

doi: 10.7151/dmgt.1632

Wai Chee Shiu
Department of Mathematics, Hong Kong Baptist University | Hong-Yu Chen
School of Mathematics and System Sciences, Shandong University | Xue-Gang Chen
Department of Mathematics, North China Electric Power University | Pak Kiu Sun
Department of Mathematics, Hong Kong Baptist University |

**Keywords:** total domination number, total restrained domination number, direct product of graphs

**2010 Mathematics Subject Classification:** 05C69.

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Received 26 April 2011

Revised 28 November 2011

Accepted 30 November 2011