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.