Restrained and Total Restrained Domination of Ladder Graphs

Telle and Proskurowksi introduced restrained domination as a vertex partition problem in partial k-tress (Algorithms for vertex partitioning problems on partial k-trees, SIAM Journal on Discrete Mathematics 10(4) (1997), 529 - 550). For a graph G(V,E), a restrained domination number is the minimum cardinality of a subset of V such that for every vertex v is an element of over bar there is a vertex in as well as in over bar adjacent to v. If satisfies an additional condition that every vertex of V has a neighbor in , then is said to be a total restrained dominating set. Minimum cardinality of is restrained, total and total restrained domination number of some ladder graphs.