# Group-Antimagic Labeling of a Class of Graphs

## Submission Type

Event

## Expected Graduation Date

2017

## Location

Center for Natural Sciences, Illinois Wesleyan University

## Start Date

4-18-2015 9:00 AM

## End Date

4-18-2015 10:00 AM

## Disciplines

Mathematics

## Abstract

For k ≥ 2, a graph G is called *Z _{k}-antimagic* if there exists a labeling of its edges f: E(G) → Z

_{k}-{0} such that the labels induced on the vertices given by the sums of the labels of the edges incident to each vertex are all distinct. For a given graph G, the

*integer antimagic spectrum*is the set of all integers k for which G is Z

_{k}-antimagic. This project focuses on characterizing the integer antimagic spectrum for a class of graphs called

*closed helms*. Our method consists of applying previous results on the existence of Z

_{k}-antimagic labelings of subgraphs of closed helms, and extending these labelings to include the remaining edges.

Group-Antimagic Labeling of a Class of Graphs

Center for Natural Sciences, Illinois Wesleyan University

For k ≥ 2, a graph G is called *Z _{k}-antimagic* if there exists a labeling of its edges f: E(G) → Z

_{k}-{0} such that the labels induced on the vertices given by the sums of the labels of the edges incident to each vertex are all distinct. For a given graph G, the

*integer antimagic spectrum*is the set of all integers k for which G is Z

_{k}-antimagic. This project focuses on characterizing the integer antimagic spectrum for a class of graphs called

*closed helms*. Our method consists of applying previous results on the existence of Z

_{k}-antimagic labelings of subgraphs of closed helms, and extending these labelings to include the remaining edges.