I-magic labelings of cubic trees and n-caterpillars

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.

Name thesis:degree_name

Master of Science (MS)

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Mathematical Sciences

Grantor dc:publisher

University of Nevada, Las Vegas

Year

2003

Author dc:creator

• Ethier, John Thomas

Contributors dc:contributor

• Michelle Schultz

Statement dc:rights

• IN COPYRIGHT. For more information about this rights statement, please visit http://rightsstatements.org/vocab/InC/1.0/

Language dc:language

English

Identifier

https://oasis.library.unlv.edu/rtds/1590

OAI identifier oai:identifier

oai:oasis.library.unlv.edu:rtds-2589