CONNECTIVITY OF COPRIME GRAPHS OVER CYCLIC GROUPS

Abstract

A coprime graph over a finite group is a representation of a finite group on a graph whose vertex set is an element of the group G and two distinct vertices  x,y element G are connected if and only if the orders of the two elements are mutually prime. This research discusses the connectivity of coprime graphs over cyclic groups and their subgroups. Since any cyclic group is isomorphic to the group Zn which is the group modulo integers, the discussion in this article utilizes the group Zn. In the previous research, has been discussed the patterns that appear on the coprime graph of group Zn  and its subgroups. Based on these patterns, the connectivity of the coprime graph over the cyclic group related to Euler, Hamilton, and Planar graphs is obtained as well as the diameter and girth of the coprime graph.