Title of Thesis
Construction Methods for Edge-Antimagic Labelings of Graphs
Abdus Salam School of Mathematical Sciences / GC
|Number of Pages|
|Keywords (Extracted from title, table of contents and
abstract of thesis)|
Labeling, mapping, edge antimagic,
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.