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On the chromatic number of the <em>AO</em>(2, <em>k </em>, <em>k</em>-1) graphs.

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.

Identiferoai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etd-3578
Date06 May 2006
CreatorsArora, Navya
PublisherDigital Commons @ East Tennessee State University
Source SetsEast Tennessee State University
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceElectronic Theses and Dissertations
RightsCopyright by the authors.

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