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Research articles

ScienceAsia 43(2017): 326-333 |doi: 10.2306/scienceasia1513-1874.2017.43.326

γ-total dominating graphs of paths and cycles

Alongkot Wongsriyaa, Nantapath Trakultraiprukb,*

ABSTRACT:     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 γt(G), is the minimum cardinality of a total dominating set of G. A total dominating set of cardinality γt(G) is called a γ-total dominating set. Let TDγ be the set of all γ-total dominating sets in G. We define the γ-total dominating graph of G, denoted by TDγ(G), to be the graph whose vertex set is TDγ, and two γ-total dominating sets D1 and D2 from TDγ are adjacent in TDγ(G) if D1=D2∖{u}∪{v} for some uD2 and vD2. In this paper, we present γ-total dominating graphs of paths and cycles.

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a Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400 Thailand
b Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120 Thailand

* Corresponding author, E-mail: n.trakultraipruk@yahoo.com

Received 28 Sep 2016, Accepted 16 Nov 2017