Mathematics professor John Lattanzio and graduate student Quan Zheng will present “Matrix Graphs and Completely Independent Critical Cliques,” parts I and II, on Thursday, December 9, and Friday December 10, 2010.

Both presentations take place at 3:30 p.m. in Stright Hall, room 229.

## Part I: Dr. Lattanzio

In this presentation, k-dimensional n-square matrices are defined and subsequently matrix graphs arise naturally. Particular matrix graphs will be constructed. An application of two dimensional matrix graphs will be discussed as they provide the only known examples of graph admitting two completely independent critical cliques.

## Part II: Dr. Lattanzio and Quan Zheng

The construction of graphs admitting two completely independent critical cliques is generalized from two dimensions to three dimensions. Using 3-dimensional matrix graphs, we demonstrate the existence of an infinite family of graphs, the members of which admit three completely independent critical cliques. It is conjectured that a similar construction, using k-dimensional n-square matrices, can be used to prove the existence of a graph admitting k completely independent critical cliques.