#### Award Date

5-2011

#### Degree Type

Thesis

#### Degree Name

Master of Science in Mathematical Science

#### Department

Mathematical Sciences

#### First Committee Member

Ebrahim Salehi, Chair

#### Second Committee Member

Peter Shiue

#### Third Committee Member

Hossein Tehrani

#### Graduate Faculty Representative

Fatma Nasoz

#### Number of Pages

39

#### Abstract

For any element h of the Natural numbers, a graph G=(V,E), with vertex set V and edge set E, is said to be h-magic if there exists a labeling of the edge set E, using the integer group mod h such that the induced vertex labeling, the sum of all edges incident to a vertex, is a constant map. When this constant is 0 we call G a zero-sum h-magic graph. The null set of G is the set of all natural numbers h for which G admits a zero-sum h-magic labeling. A graph G is said to be uniformly null if every magic labeling of G induces zero sum. In this thesis we will identify the null sets of certain classes of Planar Graphs.

#### Keywords

Combinatorial analysis; Combinatorics; Graph theory

#### Disciplines

Discrete Mathematics and Combinatorics | Mathematics

#### Language

English

#### Repository Citation

Hansen, Samuel M., "Zero-sum magic graphs and their null sets" (2011). *UNLV Theses, Dissertations, Professional Papers, and Capstones*. 1010.

https://digitalscholarship.unlv.edu/thesesdissertations/1010