Mathematics Commons^™

Restrained And Other Domination Parameters In Complementary Prisms., Wyatt Jules Desormeaux

Electronic Theses and Dissertations

In this thesis, we will study several domination parameters of a family of graphs known as complementary prisms. We will first present the basic terminology and definitions necessary to understand the topic. Then, we will examine the known results addressing the domination number and the total domination number of complementary prisms. After this, we will present our main results, namely, results on the restrained domination number of complementary prisms. Subsequently results on the distance - k domination number, 2-step domination number and stratification of complementary prisms will be presented. Then, we will characterize when a complementary prism is Eulerian or …

Chromatic Number Of The Alphabet Overlap Graph, G(2, K , K-2)., Jerry Brent Farley

Electronic Theses and Dissertations

A graph G(a, k, t) is called an alphabet overlap graph where a, k, and t are positive integers such that 0 ≤ t < k and the vertex set V of G is defined as, V = {v : v = (v₁v₂...v_k); v_i ∊ {1, 2, ..., a}, (1 ≤ i ≤ k)}. That is, each vertex, v, is a word of length k over an alphabet of size a. There exists an edge between two vertices u, …

On The Chromatic Number Of The Ao(2, K , K-1) Graphs., Navya Arora

Electronic Theses and Dissertations

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 …