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Title of Thesis

Construction Methods for Edge-Antimagic Labelings of Graphs

Author(s)

MUHAMMAD KASHIF SHAFIQ

Institute/University/Department Details
Abdus Salam School of Mathematical Sciences / GC University, Lahore
Session
2010
Subject
Mathematics
Number of Pages
82
Keywords (Extracted from title, table of contents and abstract of thesis)
Labeling, mapping, edge antimagic, graceful trees

Abstract
A labeling of a graph is a mapping that carries some set of graph elements into numbers (usually positive integers). An (a, d)-edge-antimagic total labeling of a graph, with p vertices and q edges, is a one-to-one mapping that takes the vertices and edges into the integers 1, 2, . . . , p+q, so that the sums of the label on the edges and the labels of their end vertices form an arithmetic progression starting at a and having difference d. Such a labeling is called super if the p smallest possible labels appear at the vertices.
This thesis deals with the existence of super (a, d)-edge-antimagic total labelings of regular graphs and disconnected graphs.
We prove that every even regular graph and every odd regular graph, with a 1-factor, admits a super (a, 1)-edge-antimagic total labeling. We study the super (a, 2)-edge-antimagic total labelings of disconnected graphs and present some necessary conditions for the existence of (a, d)-edge-antimagic total labelings for d even. The thesis is also devoted to the study of edge-antimagicness of trees. We use the connection between graceful labelings and edge-antimagic labelings for generating large classes of edge-antimagic total trees from smaller graceful trees.

Download Full Thesis
513 KB
S. No. Chapter Title of the Chapters Page Size (KB)
1 0 CONTENTS

 

ix
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2

1

BASIC TERMINOLOGY AND DEFINITIONS

1.1 Graph Theoretical Terminology

1.2 Antimagic Labelings

1.3 Graceful Labelings

5
185 KB
3 2 SUPER (A, D)-EDGE-ANTIMAGIC TOTAL LABELINGS FOR D EVEN

2.1 Super (A, 2)-Edge-Antimagic Total Labelings For The Disjoint Union Of Graphs

2.2 Conditions for non-existence of (super) (a, d)-edge-antimagic total labelings

21
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4 3 SUPER (A, D)-EDGE-ANTIMAGIC TOTAL LABELINGS FOR D ODD

3.1 Super (a, 1)-edge-antimagic total labelings for regular graphs

3.2 Super (a, 1)-edge-antimagic total labelings for non-regular graphs

33
135 KB
5 4 GENERATING LARGE CLASSES OF EDGE-ANTIMAGIC TOTAL TREES

4.1 Connections between -labelings and edgeantimagic vertex labelings for trees

4.2 Construction of -tree from smaller graceful trees

4.3 Generating edge-antimagic trees

4.4 Certain families of super (a, d)-edge-antimagic total trees

43
174 KB
6 5 BIBLIOGRAPHY & APPENDICES

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