

Title of Thesis
Construction Methods for EdgeAntimagic 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)edgeantimagic total
labeling of a graph, with p vertices and q edges, is a onetoone
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)edgeantimagic
total labelings of regular graphs and disconnected graphs.
We prove that every even regular graph and every odd regular graph,
with a 1factor, admits a super (a, 1)edgeantimagic total
labeling. We study the super (a, 2)edgeantimagic total labelings
of disconnected graphs and present some necessary conditions for the
existence of (a, d)edgeantimagic total labelings for d even. The
thesis is also devoted to the study of edgeantimagicness of trees.
We use the connection between graceful labelings and edgeantimagic
labelings for generating large classes of edgeantimagic total trees
from smaller graceful trees.

