الفهرس 
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Abstract
In this thesis we are concerned with a very important topic in graph
theory, which is graph labeling. We study seven labelings of graphs,
combination labeling, divisor labeling, divisor cordial labeling, -divisor
labeling, square sum labeling, perfect square sum labeling, and strongly
square sum labeling. This thesis consists of four chapters.
In Chapter one, we introduce some basic definitions and notations in
graph theory which we will need afterwards. Also, we deal with
preliminary definitions and results about the related work in this thesis
which have been done before.
In Chapter two, we study combination graphs. We introduce some
theorems for a graph to be a non-combination graph, and some theorems
on chains of two and three complete graphs, considering when they are
combination or non-combination graphs. Also we present some families
of combination graphs. Finally we give a survey for trees of order
≤ 10, which are all combination graphs.
In Chapter three, we discuss three kinds of divisor graphs, namely the
usual divisor graph, the divisor cordial graph and a new divisor graph
called - divisor graph.
In Chapter four, we introduce a type of labeling of graphs which is
closely related to the Diophantine Equation + . We introduce
some families to be square sum graphs. We determine the number of
strongly square sum graphs corresponding to the number of edges. We
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present a program finding the maximum number of edges of square sum
and perfect square sum graphs.
List of publications arising from this thesis
[1] M. A. Seoud , M.N. Al-Harere, Some Notes on Combination Graphs,
accepted for publication in Ars Combinatoria.
[2] M.A.Seoud, M.N. Al-Harere ,On Combination Graphs,
Int.Math.Forum ,7(2012)1767-1776.
[3] M. A. Seoud , M.N. Al-Harere, Some Non-Combination Graphs,
Applied Mathematical Sciences, 6( 2012), 6515 - 6520 .
[4] M. A. Seoud , M.N. Al-Harere, Three Kinds of Divisor Graphs,
preprint.
[5] M. A. Seoud , M.N. Al-Harere, Further Results on Square Sum
Graphs, accepted for National Academy Science Letters, Springer.