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The Knill Graph Dimension From Clique Cover, Evatt Salinger, Dr. Kassahun Betre
The Knill Graph Dimension From Clique Cover, Evatt Salinger, Dr. Kassahun Betre
Seaver College Research And Scholarly Achievement Symposium
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.