Total and paired domination numbers of toroidal meshes

Authors:
Fu-Tao Hu;Jun-Ming Xu
Affiliations:
School of Mathematical Sciences, Anhui University, Anhui, P.R. China 230601;School of Mathematical Sciences, Wentsun Wu Key Laboratory of CAS, University of Science and Technology of China, Anhui, P.R. China 230026
Venue:
Journal of Combinatorial Optimization
Year:
2014

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Abstract

Let G be a graph without isolated vertices. The total domination number of G is the minimum number of vertices that can dominate all vertices in G, and the paired domination number of G is the minimum number of vertices in a dominating set whose induced subgraph contains a perfect matching. This paper determines the total domination number and the paired domination number of the toroidal meshes, i.e., the Cartesian product of two cycles C n and C m for any n驴3 and m驴{3,4}, and gives some upper bounds for n,m驴5.