Date : March 23, 2023, 1:30 p.m. - Room :Amphi 3 - Pôle commun

Total Domination in Graphs

Michael HENING, Professeur - Université de Johannesbourg

A total dominating set in a graph G is a set of vertices of G such that every vertex is adjacent to a vertex of the set. The total domination number \gamma_t(G) is the minimum cardinality of a dominating set in G. We present selected results on total domination in graphs. We discuss bounds on the size (number of edges) of a graph in terms of its order (number of vertices) and total domination number. We present best known bounds to date on the total domination number of a graph with given minimum degree in terms of the order of the graph, and show how the powerful tool of transversal in hypergraphs can be used to obtain results on total domination in graphs.