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

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Mar 29th, 2:00 PM Mar 29th, 3:00 PM

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.