Moss, Elena2022-06-292022-06-2920222022-06-29http://hdl.handle.net/1828/14003There are a wide variety of problems in graph domination. We discuss eternal paired domination in trees, a variation which requires guards stationed at the vertices of a dominating set to be able to defend against any sequence of attacks, while the guards remain adjacent to a “buddy” at all times. We have found an algorithm to obtain such a decomposition and proved that it is minimum. The eternal paired domination number of any non-trivial tree T is 2γ(T), where γ(T) is the domination number of T. Finally, we provide a counterexample in split graphs to demonstrate that this strategy cannot generalize to all chordal graphs.engraph theoryeternal dominationdynamic dominating setstreesstarsPosterDepartment of Mathematics and Statistics