MS (Master of Science)
Date of Award
Committee Chair or Co-Chairs
Debra J. Knisley
Teresa W. Haynes, Anant P. Godbole
The alphabet overlap graph is a modification of the well known de Bruijn graph. De Bruijn graphs have been highly studied and hence many properties of these graphs have been determined. However, very little is known about alphabet overlap graphs. In this work we determine the chromatic number for a special case of these graphs.
We define the alphabet overlap graph by G = AO(a, k, t, where a, k and t are positive integers such that 0 ≤ t ≤ k. The vertex set of G is the set of all k-letter sequences over an alphabet of size a. Also there is an edge between vertices u, v if and only if the last t letters in u match the first t letters in v or the first t letters in u match the last t letters in v. We consider the chromatic number for the AO(a, k, t graphs when k > 2, t = k - 1 and a = 2.
Thesis - Open Access
Arora, Navya, "On the chromatic number of the AO(2, k , k-1) graphs." (2006). Electronic Theses and Dissertations. Paper 2214. http://dc.etsu.edu/etd/2214
Copyright by the authors.