Annals of Pure and Applied Mathematics Annals of Vol. 4, No.1, 2013, 43-91 ISSN: 2279-087X (P), 2279-0888(online) Published on 1October 2013 www.researchmathsci.org Intersection Graphs: An Introduction Madhumangal Pal Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University, Midnapore – 721102, India e-mail:
[email protected] Received 1 September 2013; accepted 27 September 2013 Abstract. Intersection graphs are very important in both theoretical as well as application point of view. Depending on the geometrical representation, different type of intersection graphs are defined. Among them interval, circular-arc, permutation, trapezoid, chordal, disk, circle graphs are more important. In this article, a brief introduction of each of these intersection graphs is given. Some basic properties and algorithmic status of few problems on these graphs are cited. This article will help to the beginners to start work in this direction. Since the article contains a lot of information in a compact form it is also useful for the expert researchers too. Keywords: Design and analysis of algorithms, intersection graphs, interval graphs, circular-arc graphs, permutation graphs, trapezoid graphs, tolarence graphs, chordal graphs, circle graphs, string graphs, disk graphs AMS Mathematics Subject Classification (2010): 05C62, 68Q22, 68Q25, 68R10 1. Introduction It is well known that graph is a very useful tool to model problems originated in all most all areas of our life. The geometrical structure of any communication system including Internet is based on graph. The logical setup of a computer is designed with the help of graph. So graph theory is an old as well as young topic of research.