γ-total dominating graphs of paths and cycles
Alongkot Wongsriya, Nantapath Trakultraipruk · ScienceAsia · 2017
is adjacent to some vertex in D. The total domination number of G, denoted by γ t (G), is the minimum cardinality of a total dominating set of G.A total dominating set of cardinality γ t (G) is called a γ-total dominating set.Let T D γ be the set of all γ-total dominating sets in G.We define the γ-total dominating graph of G, denoted by T D γ (G), to be the graph whose vertex set is T D γ , and two γ-total dominating sets D 1 and D 2 from T D γ are adjacent in T D γ (G) if D 1 = D 2 \{u} ∪ {v} for some u ∈ D 2 and v / ∈ D 2 .In this paper, we present γ-total dominating graphs of paths and cycles.