A Study On Neighbourhood Domination in Interval Family and Circular ARC Family of Graphs Using Algorithms

Abstract

Research in Graph Theory and its applications have increased considerably in recent years. Typically, the elaboration of new theoretical structures has motivated a research for new algorithms compatible with those structures. Rather than the arduous and systematic study of every new concept definable with a graph corresponding interval graph as well as circular arc graph, the main task for the Mathematician is to eliminate the often arbitrary and cumbersome definitions, keeping only the and#8242;and#8242;deepand#8242;and#8242; Mathematical problems. newlineThe basic ideas of Graph Theory were introduced during 18th century by the great mathematician Leonard Euler. Since then relatively in a short period the major development of graph theory has occurred and inspired to a larger degree and it has become the source of interest to many researchers. To some extent this may be due to the ever growing importance of computer science and its connection with graph theory. Graph Theory is a fascinating subject. Today graph theory is one of the most flourishing branches of modern Mathematics. The last 30 years have witnessed spectacular growth of graph theory due to its wide applications to discrete optimization problems, combinatorial problems, and classical algebraic problems. One simple way of representing the structure of a system is to use graphs, which are simple diagrams consisting of points(vertices) and lines(edges). Graphs are useful in enhancing the understanding of the organization and behavioural characteristics of computer systems. Its rigour and Mathematical elegance appear in problem solving. Problems in almost every conceivable disciple can be solved using graph models. It has a very wide range of applications to many fields like engineering, physical, social and biological sciences, Linguistics, etc. newline newlineThe subject of graph theoretic algorithms is as old as graph theory itself, which is usually regarded as having started with Euler s famous solution of the problem of the seven bridges of Konigsberg.