#### Degree Name

MS (Master of Science)

#### Program

Mathematical Sciences

#### Date of Award

5-2006

#### Committee Chair or Co-Chairs

Debra J. Knisley

#### Committee Members

Teresa W. Haynes, Anant P. Godbole

#### Abstract

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.

#### Document Type

Thesis - Open Access

#### Recommended Citation

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

Copyright by the authors.