Department of Mathematics
Some results on matching and total domination in graphs
Let G be a graph. A set S of vertices of G is called a total dominating set of G if every vertex of G is adjacent to at least one vertex in S. The total domination number γt(G) and the matching number α'(G) of G are the cardinalities of the minimum total dominating set and the maximum matching of G, respectively. In this paper, we introduce an upper bound of the difference between γt(G) and α'(G). We also characterize every tree T with γt(T) ≤ α'(T), and give a family of graphs with γt(G) ≤ α'(G).
Induced matching number, Matching number, Total domination number
Source Publication Title
Applicable Analysis and Discrete Mathematics
University of Belgrade and Academic Mind
Shiu, Wai Chee, Xue-gang Chen, and Wai Hong Chan. "Some results on matching and total domination in graphs." Applicable Analysis and Discrete Mathematics 4.2 (2010): 241-252.