Application of Graph Theory in Computer Science and Engineering
Dr. Vasanthakumari T.N.
Assistant Professor
Department of Mathematics
Government First Grade College, Tumakuru, Karnataka
ABSTRACT
The field of mathematics plays vital role in various fields. One of the important areas in mathematics is graph theory which is used in structural models. This structural arrangements of various objects or technologies lead to new inventions and modifications in the existing environment for enhancement in many fields. The field graph theory started its journey from the problem of Koinsberg Bridge in 1735. This paper gives an overview of the applications of graph theory in many different fields to some extent but mainly focuses on the computer science applications that uses graph theoretical concepts. Various papers and related works based on graph theory have been studied and implemented for this scheduled concepts, computer science applications.
KEY WORDS: Graph Theory, Koinsberg Bridge, mathematical structures, Data base design
INTRODUCTION
Graph theory is a branch of discrete mathematics. In mathematics and computer science, graph theory is the study of graphs which are mathematical structures used to model pair wise relations between objects. There is wide use of graphs in providing problem solving techniques, because it gives an intuitive manner prior to presenting formal definition. To analyze the graph theory application two problem areas are considered.
The classical problem are defined with the help of the graph theory as connectivity, cuts, paths and flows, coloring problems and theoretical aspect of graph drawing. Whereas problems from application particularly emphasis on experimental research and the implementation of the graph theory algorithms. Graph drawing is a key topic in implementation point of view, because the automatic generation of drawing graph has important applications in key computer science technologies such as data base design, software engineering, circuit designing, network designing and visual interfaces.
APPLICATION IN COMPUTER SCIENCE:
Data base designing:
In data base designing graphs are used as graph data bases. Graph database uses graph representation with nodes, edges, and properties to represent and store data. This graph structure has key role in designing database, because it gives fast implementation process using different functionality and properties of graph structure .Graph database uses as:
Software engineering:
Graph has many applications in software engineering. For example: during Requirements Specification, Data Flow diagrams are used where vertices represent transformations and edges represents the data flows. During Design phase, graphical design is used for describing relations among modules; while during Testing, the control flow of a program associated with McCabe's complexity measure which employs directed graphs for addressing the sequence of executed instructions and etc. Even Software Process Management has also applications of network diagrams which involves graph algorithms.
Network system:
Graph theory has wide application in the field of networking. To analyze the graph theory application in networking two areas are considered: graph based representation and network theory. Graph based representation has many advantages such as it gives different point of view; it makes problem much easier and provide more accurate definition. Whereas network theory provide a set of techniques for analyzing a graph and applying network theory using a graph representation. The term graph and network are equal. Both refer to a type of structure in which there exists vertices (i.e. nodes, dots) and edges (i.e. links, lines). There are numerous types of graphs and networks which yield more or less structure. These two terms can be differentiating on the basis of their utility.
Data structure:
Data may be organized many different ways. The logical or mathematical model of a particular organization of data is called a “data structure”. The choice of data model depends on two considerations:
These two considerations is fulfilled by the graph theoretical concepts. Arbitrary relation among data can also be represented by a graph and its matrices , operations performed on these metrics are further useful for deriving relations and data association and is useful in order to understand how these data may be stored in memory.
Conclusion:
The fundamental rationale of this paper is to present the significance of the graph theoretical thoughts in various fields of computer applications for exploring that they can utilize graph theoretical concepts for the examination. An outline is exhibited particularly to extend graph theory. Analysts may make them inspire data to graph theory and its applications in the computer field and get a few contemplations identified with their territory of research.
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