www.ijesrr.org Page 9 Effect of Basic Set Operations on Graph Theory

Graph theory has strong historical roots in Mathematics. Its birth is usually associated with the four-color problem posed by Francis Guthrie in 1852, but its real origin probably goes back to the Seven Bridges of Konigsberg Problem proved by Leonhard Euler in 1736. In general, a graph is a nonempty set of points (vertices) and the most basic information preserved by any graph structure refers to adjacency relationships (edges) between some pairs of points. In the simplest graphs, edges do not have to hold any attributes, except their endpoints, but in more sophisticated graph structures, edges can be associated with a direction or assigned a label. There are several reasons for the acceleration of interest in graph theory. Graph theory has aspects that connect it with other areas of Mathematics such as algebra, geometry, topology, numerical analysis, matrix theory, and combinatory and so on. The expressive power of the graph models placing special emphasis on connectivity between objects has made them the models of choice in chemistry, physics, biology, and other fields. Graph theory is a young but rapidly maturing subject. Within the quarter of a century, concurrent with the growth of such areas as computer science, electrical and computer engineering, and operations research, graph theory has seen explosive growth. Perhaps the fastest-growing area within graph theory is the study of domination, topological graph theory, coloring theory, and related subset problems