eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 2019-06-06 7 3 77 84 10.12691/tjant-7-3-4 TJANT2019734 article M. A. Rajan 1 Kinkar Ch. Das kinkardas2003@googlemail.com 2 V. Lokesha 3 I. Naci Cangül 4 Innovation Labs, Tata Consultancy Services Ltd, Abhilash, A Block 3rd Floor,EPIP IndustrialArea, Whitefield, Bangalore-560066, Karnataka, India Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea Department of Mathematics, Vijayanagara Sri Krishnadevaraya University, Bellari, Karnataka, India Department of Mathematics, Faculty of Science, Uludag University, Görükle, 16059, Bursa, Turkey A is a labelled graph denoted by in which the vertex set of an has vertices labeled {} and edges such that there exist an edge between two distinct vertices labeled { and }, if { and } are coprime to each other. In this paper, some properties of the ER- are studied. An algorithm to compute GCD and LCM of any two numbers between and p by means of an ER- graph is also described. http://pubs.sciepub.com/tjant/7/3/4/tjant-7-3-4.pdf Euler's phi-function coprime prime number chromatic number co-prime graph