A set S of vertices in a graph G is a total dominating set of G if every vertex of G is adjacent to some vertex in S. We characterize the set of vertices of a tree that are contained in all, or in no, minimum total dominating sets of the tree. © 2002 Elsevier Science B.V. All rights reserved.
Cockayne, E. J., Henning, M. A., & Mynhardt, C. M. (2003). Vertices contained in all or in no minimum total dominating set of a tree. Discrete Mathematics, 260(1–3), 37–44. https://doi.org/10.1016/s0012-365x(02)00447-8