Date of Award

Spring 5-2015

Degree Type

Honors College Thesis



First Advisor

Samuel Jeremy Lyle

Advisor Department



Using information provided by Ryan Pepper and Ermelinda DeLaVina in their paper On the 2-Domination number and Annihilation Number, I developed a new bound on the 2- domination number of trees. An original bound, γ2(G) ≤ (n+n1)/ 2 , had been shown by many other authors. Our goal was to generate a tighter bound in some cases and work towards generating a more general bound on the 2-domination number for all graphs. Throughout the span of this project I generated and proved the bound γ2(T ) 1/3 (n + 2n1 + n2). To prove this bound I first proved that the 2-domination number of a tree was less than or equal to the sum of two sub-trees formed by the deletion of an edge: γ2(T ) γ2(T1) + γ2(T2). From there, I proved our bound by showing that a minimum counter-example did not exist. A large portion of the results involves cases where a graph T is considered the minimum counter-example for the sake of contradiction. From there, I showed that if T was a counter-example, then a sub-tree T1 was also a counter-example, meaning that T would no longer be the minimum counter-example. The last portion of the results is a section comparing the two bounds on the 2-domination number with respect to the number of edges and the degrees of those edges.