Study of All Powers of Paths and Cycles Towards Domination

Several researchers for over 25 years are drawn towards the interval graphs. Extensive studies and the consequent revelations underlined their practical relevance to a number of real time modeling problems. Their presence is steadily enhancing in the literature pertaining to interval graphs and at times they claim to be the most studied categories of graphs. This could be partly due to the fact that interval graphs are being utilized in a number of applications related to different areas such as biology, archaeology, psychology, genetics, traffic control, database, artificial intelligence, computer scheduling, retrieval of storage information and electronic circuit design etc. In addition, interval graphs are reputed among the community of graph theory due to the vast range of properties arising out of their simple structure. we find the formulas to find domination number, chromatic number and total domination number of all powers of cycles using a circular-arc graph G. And we find algorithms to find domination number and total domination number of all powers of cycles using a circular-arc graph G