Total Domination Cover Rubbling
Let G be a connected simple graph with vertex set V and a distribution of pebbles on the vertices of V. The total domination cover rubbling number of G is the minimum number of pebbles, so that no matter how they are distributed, it is possible that after a sequence of pebbling and rubbling moves, the set of vertices with pebbles is a total dominating set of G. We investigate total domination cover rubbling in graphs and determine bounds on the total domination cover rubbling number.
Beeler, Robert A.; Haynes, Teresa W.; Henning, Michael A.; and Keaton, Rodney. 2020. Total Domination Cover Rubbling. Discrete Applied Mathematics. Vol.283 133-141. https://doi.org/10.1016/j.dam.2019.12.020 ISSN: 0166-218X