Award Date

1-1-2003

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematical Sciences

First Committee Member

Michelle Schultz

Number of Pages

53

Abstract

Let G be a graph with q edges, then an edge labeling L: E → {1, 2,.., q} is a bijection from the set of edges E to the set of natural numbers less than or equal to q. A graph is said to be I-magic if there exists an edge labeling such that the sum of all edge labels incident to each internal vertex has the same value, and this value is called the magic index t, while the labeling is called an I-magic labeling. It has been conjectured that all cubic trees are I-magic. In this paper, we develop methods for finding I-magic labelings and determine boundary conditions for the magic index of given tRees We also classify an infinite subclass of cubic trees which are I-magic, namely cubic caterpillars. Furthermore, we classify all n-caterpillars as I-magic for n ≥ 3.

Keywords

Caterpillars; Cubic Labelings; Magic Trees

Controlled Subject

Mathematics

File Format

pdf

File Size

1146.88 KB

Degree Grantor

University of Nevada, Las Vegas

Language

English

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