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 \(D\) of \(V\) such that for every vertex \(vD \) there is a vertex in \(D\) as well as in \(D \) adjacent to \(v\). If \(D\) satisfies an additional condition that every vertex of \(V\) has a neighbor in \(D\), then \(D\) is said to be a total restrained dominating set. Minimum cardinality of \(D\) is said to be total restrained domination number of graph \(G\). In this paper we have obtained domination, restrained, total and total restrained domination number of some ladder graphs. , number=4, journal=Communications in Mathematics and Applications, author=Hemalatha, N. C. and Chandrakala, S. B. and Sooryanarayana, B. and Kumar, M. Vishu, year=2023, month=Dec., pages=1311–1323