الفهرس 
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Abstract
The project of this thesis concerns a field of mathematics called geometric topology.
The main purpose of this thesis is to study some new graphs and their variations.
The thesis is divided into five chapters:
Chapter One: Basic concepts
In chapter (1) is an introduction and presents a brief survey of main important
definitions that help us in our work.
Chapter two: The Graph Of Simplex Vertices
In chapter (2) we will introduce a new types of graph. The representation of the
new graph by adjacent and incidence matrices will be obtained. Some geometric
transformations(Folding) on the new graphs are described.
The results of this chapter were published in ”Journal of Mathematics
research” (Vol. 4, No. 1; February 2012) In Canada.
Chapter three: The Retraction Of Graph with simplex Vertices.
In chapter (3) we will discuss the retraction of new graph in which its vertices are
simplexes. The limit of these retractions is obtained . Some theorems related to these
transformations are proved. The effect of retraction on adjacent and incident matrices
will be deduced.
The results of this chapter are accepted for publication in ”International Journal
Computational And Applied Mathematics”. In India. Of
Chapter four: Neighborhoods Of The Undirected Graph With
Simplex Vertices.
In chapter (4) we will compute first and second neighborhood for new undirected
graph with simplex vertices. Some theorems related to this subject are obtained. We
also introduced some examples on 0-simplex,1-simplex,2-simplex and n-simplex.
The results of this chapter are accepted for publication in ”International Journal
Of Applied Science and Technology”. In United States Of America.
Chapter five: Neighborhoods Of Directed Simplex Graph.
In chapter (5) we will compute first and second neighborhood for directed simplex
graph. Some theorems related to this subject are obtained. We also introduced some
examples on 0-simplex,1-simplex,2-simplex and n-simplex.
The results of this chapter were published in ”International Journal Of
In India. 2012) April ; Vol. 3, No. 4 ( ” Archive Mathematics.