#### Abstract

This paper includes some basic ideas about the computation of a function theta(G), the theta number of a graph G, which is known as the Lovasz number of G. theta(G^c) lies between two hard-to-compute graph numbers omega(G), the size of the largest lique in a graph G, and chi(G), the minimum number of colors need to properly color the vertices of G. Lovasz and Grotschel called this the "Sandwich Theorem". Donald E. Knuth gives four additional definitions of theta, theta_1, theta_2, theta_3, theta_4 and proves that they are all equal.

First I am going to describe the proof of the equality of theta, theta_1 and theta_2 and then I will show the calculation of the theta function for some specific graphs: K_n, graphs related to K_n, and C_n. This will help us understand the theta function, an important function for graph theory. Some of the results are calculated in different ways. This will benefit students who have a basic knowledge of graph theory and want to learn more about the theta function.

#### Degree

MS

#### College and Department

Physical and Mathematical Sciences; Mathematics

#### Rights

http://lib.byu.edu/about/copyright/

#### BYU ScholarsArchive Citation

Riddle, Marcia Ling, "Sandwich Theorem and Calculation of the Theta Function for Several Graphs" (2003). *All Theses and Dissertations*. 57.

https://scholarsarchive.byu.edu/etd/57

#### Date Submitted

2003-03-17

#### Document Type

Thesis

#### Handle

http://hdl.lib.byu.edu/1877/etd181

#### Keywords

combinatorics, graph theory, theta function, sandwich theorem, feasible matrix, Lovasz number

#### Language

English