Please join us welcoming Ph.D student Justin Wisby for this week's graduate student seminar.  

Our Graduate Student Seminar gives students the ability to showcase interesting results that they have found in their research. Presenters are typically graduate students in mathemathematics, but can also be undergraduates, students in other disiplines, and faculty as well. 

Presentations should be able to be understood by undergraduate students in mathematics or related disipline.

Abstract: Let G = (V (G), E(G)) be a finite undirected graph. A set S of vertices in
V is said to be total k-dominating if every vertex in V is adjacent to at least k vertices
in S. The k-domination number, γk (G), is the minimum cardinality of a k-dominating
set in G. In this work we study the k-domination number of Cartesian products of two
complete graphs, which is a lower bound of the total k-domination number of Cartesian
product of any two graphs with the same number of vertices. We obtain new lower and
upper bounds for the k-domination number of Cartesian product of two complete graphs.
Some asymptotic behaviors are obtained as a consequence of the bounds we found.