Geodesic
On the total domination number of total graphs
Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 3, pp. 933-951

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Let G be a graph with no isolated vertex. A set D⊆ V(G) is a total dominating set of G if every vertex of G is adjacent to at least one vertex in D. The total domination number of G, denoted by γ_t(G), is the minimum cardinality among all total dominating sets of G. In this paper we study the total domination number of total graphs T(G) of simple graphs G. In particular, we give some relationships that exist between γ_t(T(G)) and other domination parameters of G and of some well-known graph operators on G. Finally, we provide closed formulas on γ_t(T(G)) for some well-known families of graphs G.
Keywords: total domination, graph operators, total graphs 
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     title = {On the total domination number of total graphs},
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Cabrera-Martínez, Abel; Sánchez, José L.; Sigarreta Almira, Jośe M. On the total domination number of total graphs. Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 3, pp. 933-951. http://geodesic.mathdoc.fr/item/DMGT_2024_44_3_a6/