Rumus Umum Pelabelan L(2, 1) pada Graf Koprima Grup Bilangan Bulat Modulo m

Groups are nonempty sets equipped with binary operations and fulfill certain conditions. One example of a group is the group of integers modulo . A coprime graph of a group is a graph whose vertices are elements in and any two vertices in are directly connected if and only if the greatest common factor of the orders x and y are relatively prime. labeling has important applications in wireless telecommunication networks, where there are limited radio frequencies available and adjacent transmitters cannot use the same frequency. To overcome this problem, frequency assignment is done using the concept of labeling, where transmitters are symbolized as vertices connected by edges. labeling is a graph labeling technique that assigns non-negative integer labels to graph vertices with the rule that two directly connected vertices must have a minimum label difference of two, and two vertices that are two apart must have a minimum label difference of one. The purpose of this research is to find out the general formula for the labeling on the coprime graph of the group of integers modulo and the general formula for the minimum value of the largest label of the labeling. The steps taken in this research are to determine the coprime graph form of the group of integers modulo . Then label each vertex with a non-negative label. Then label each vertex with labeling rule. From the result of this research, it can be concluded that the coprime graph of integer group modulo has a labeling with .