I-magic labelings of cubic trees and n-caterpillars
type: CreativeWork
description: 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.
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.
author: Ethier, John Thomas
language: English
date published: 2003-01-01T08:00:00Z
date modified: 2026-07-24T05:25:40Z
provider: University of Nevada - Las Vegas
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of Nevada, Las Vegas

PropertyValue
property ID: DOI
value: 10.25669/zs5c-3kpc