On planar graphs

The aim of this thesis is to study planar graphs. A graph G is called a planar graph if G can be drawn in the plane without any two of its edges crossing. Our study consists of four chapters. The first two sections, Introduction and Literature Survey, discuss the historical works on graphs. In the third section, the basic concepts of graph and graph types, basic definitions, and theorems that we will use in our calculations are given. In the fourth section, the definition of a planar graph is given and some special planar graphs are given. Euler's formula is introduced and Euler's formula is used to determine whether a graph is planar or not. Non-planar graphs have been given with the help of different theorems and examples. Embedding a graph in a plane has given. The concepts of region and map in graphs were given and the definition of the degree of region of graphs and examples were given. Edge and node constriction in graphs are given. Examples of Platonic objects are given and the example of transforming Platonic objects into graphs is discussed. In addition, five smooth polyhedra, which are examples of these fields, are given. The concept of the minor in graphs is defined and examples are given. The concepts of interior node and intersection in graphs and examples are given. The concept of maximal planar graph and examples are given. The definition of an outer planar graph is given and examples are given. In this section, planar graphs are analyzed.