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Title of Thesis

Face Labelings of Graphs

Author(s)

FOZIA BASHIR

Institute/University/Department Details
Abdus Salam School of Mathematical Sciences / GC University, Lahore
Session
2010
Subject
Mathematics
Number of Pages
78
Keywords (Extracted from title, table of contents and abstract of thesis)
Face, Labelings, Graphs, Sampling, literature, household

Abstract
The thesis deals with the problem of labeling the vertices, edges and faces of a plane graph in such a way that the label of a face and the labels of vertices and edges surrounding that face add up to a weight of that face. A labeling of a plane graph is called d-antimagic if for every positive integer s, the s-sided face weights form an arithmetic progression with a di erence d. Such a labeling is called super if the smallest possible labels appear on the vertices. The thesis is devoted to study of super d-antimagic labelings of type (1; 1; 1) for antiprisms and disjoint union of prisms.
We consider the antiprism and prism as three cycle parts: the outer cycle, the inner cycle and the middle cycle. To label the inner, the outer and the middle cycles we use the edge-antimagic total labelings and the vertex-antimagic total labelings. These labelings combine to a resulting super d-antimagic labeling of type (1; 1; 1) for the required values of di erence d.

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

 

vii
57.1 KB
2

1

MAGIC AND ANTIMAGIC LABELINGS

1.1 Basic de nitions

1.2 Magic-type labelings

1.3 Antimagic-type labelings

5
168 KB
3 2 LABELINGS FOR 2-REGULAR GRAPHS

2.1 Labelings for cycles

2.2 Labelings for union of cycles

19
193 KB
4 3 FACE ANTIMAGIC LABELINGS OF ANTIPRISMS

3.1 Necessary conditions

3.2 Antiprism as three cycle parts

3.3 d-antimagic labelings of antiprism

31
171 KB
5 4 FACE ANTIMAGIC LABELINGS OF DISJOINT UNION OF PRISMS

4.1 Necessary conditions

4.2 mDn decomposed into 3m disjoint cycles

4.3 d-antimagic labelings of mDn

45
199 KB
6 5 CONCLUSION, BIBLIOGRAPHY & APPENDICES

59


110 KB