γ-total dominating graphs of lollipop, umbrella, and coconut graphs

A total dominating set of a graph G is a set D subset of V ( G ) such that every vertex of G is adjacent to some vertex in D . The total domination number gamma t ( G ) of G is the minimum cardinality of a total dominating set. The gamma -total dominating graph TD gamma ( G ) of G is the graph whose vertices are minimum total dominating sets, and two minimum total dominating sets of TD gamma ( G ) are adjacent if they differ by only one vertex. In this paper, we determine the total domination numbers of lollipop graphs, umbrella graphs, and coconut graphs, and especially their gamma -total dominating graphs.