16 th Int. Conf. on IFSs, Sofia, 9–10 Sept. 2012 Notes on Intuitionistic Fuzzy Sets Vol. 18, 2012, No. 3, 52–60 Properties of intuitionistic fuzzy line graphs M. Akram 1 and R. Parvathi 2 1 Punjab University College of Information Technology, University of the Punjab Old Campus, Lahore-54000, Pakistan e-mails: makrammath@yahoo.com, m.akram@pucit.edu.pk 2 Department of Mathematics, Vellalar College for Women Erode – 638 012, Tamilnadu, India e-mail: paarvathis@rediffmail.com Abstract: Concepts of graph theory have applications in many areas of computer science includ- ing data mining, image segmentation, clustering, image capturing, networking. An intuitionistic fuzzy set is a generalization of the notion of a fuzzy set. Intuitionistic fuzzy models give more precision, flexibility and compatibility to the system as compared to the fuzzy models. In this paper, we investigate some interesting properties of intuitionistic fuzzy line graphs. Keywords: Intuitionistic fuzzy intersection graph, intuitionistic fuzzy line graphs. AMS Classification: 05C99. 1 Introduction In 1736, Euler first introduced the concept of graph theory. In the history of mathematics, the solution given by Euler of the well known K¨ onigsberg bridge problem is considered to be the first theorem of graph theory. This has now become a subject generally regarded as a branch of combinatorics. The theory of graph is an extremely useful tool for solving combinatorial prob- lems in different areas such as geometry, algebra, number theory, topology, operations research, optimization and computer science. In 1983, Atanassov [6] introduced the concept of intuitionistic fuzzy sets as a generalization of fuzzy sets [16]. Atanassov added a new component(which determines the degree of non- membership) in the definition of fuzzy set. The fuzzy sets give the degree of membership of an element in a given set (and the non-membership degree equals one minus the degree of mem- bership), while intuitionistic fuzzy sets give both a degree of membership and a degree of non- 52