#### Presentation Title

#### Presentation Type

Poster

#### Keywords

Oliver, Knill, Graph, Dimension, Clique, Cover, Union, Graph theory, Recursive, Join, Betre, Salinger, Evatt, Join

#### Department

Physics

#### Major

Physics

#### Abstract

In this paper we prove that the recursive (Knill) dimension of the join of two graphs has a simple formula in terms of the dimensions of the component graphs: dim (G1 + G2) = 1 + dim G1 + dim G2. We use this formula to derive an expression for the Knill dimension of a graph from its minimum clique cover. A corollary of the formula is that a graph made of the arbitrary union of complete graphs KN of the same order KN will have dimension N − 1.

#### Faculty Mentor

Dr. Kassahun Betre

#### Funding Source or Research Program

Academic Year Undergraduate Research Initiative

#### Location

Waves Cafeteria

#### Start Date

29-3-2019 2:00 PM

#### End Date

29-3-2019 3:00 PM

#### Included in

The Knill Graph Dimension from Clique Cover

Waves Cafeteria

In this paper we prove that the recursive (Knill) dimension of the join of two graphs has a simple formula in terms of the dimensions of the component graphs: dim (G1 + G2) = 1 + dim G1 + dim G2. We use this formula to derive an expression for the Knill dimension of a graph from its minimum clique cover. A corollary of the formula is that a graph made of the arbitrary union of complete graphs KN of the same order KN will have dimension N − 1.