Trees with Unique Minimum Semitotal Dominating Sets
A set S of vertices in a graph G is a semitotal dominating set of G if it is a dominating set of G and every vertex in S is within distance 2 of another vertex of S. The semitotal domination number is the minimum cardinality of a semitotal dominating set of G. We observe that the semitotal domination number of a graph G falls between its domination number and its total domination number. We provide a characterization of trees that have a unique minimum semitotal dominating set.
Haynes, Teresa W.; and Henning, Michael A.. 2020. Trees with Unique Minimum Semitotal Dominating Sets. Graphs and Combinatorics. Vol.36(3). 689-702. https://doi.org/10.1007/s00373-020-02145-0 ISSN: 0911-0119