γ-total dominating graphs of paths and cycles

A total dominating set for a graph G = (V(G), E(G)) is a subset D of V(G) such that every vertex in V(G) is adjacent to some vertex in D. The total domination number of G, denoted by gamma(t) (G), is the minimum cardinality of a total dominating set of G. A total dominating set of cardinality gamma(t) (G) is called a gamma-total dominating set. Let TD gamma be the set of all gamma-total dominating sets in G. We define the gamma-total dominating graph of G, denoted by T D-gamma (G), to be the graph whose vertex set is T D-gamma, and two gamma-total dominating sets D1 and D2 from T D-gamma are adjacent in T D-gamma (G) if D-1 = D-2 \{u} boolean OR {v} for some u is an element of D-2 and v is not an element of D-2. In this paper, we present gamma-total dominating graphs of paths and cycles.