Frequency Assignment Model of Zero Divisor Graph

Given a frequency assignment network model is a zero divisor graph of commutative ring , in this model, each node is considered to be a channel and their labelings are said to be the frequencies, which are assigned by the and labeling constraints. For a graph , labeling is a nonnegative real valued function such that if and if where and are any two vertices in and is a distance between and . Similarly, one can extend this distance labeling terminology up to the diameter of a graph in order to enhance the channel clarity and to prevent the overlapping of signal produced with the minimum resource (frequency) provided. In general, this terminology is known as the labeling where is the difference of any two vertex frequencies connected by a two length path. In this paper, our aim is to find the minimum spanning sharp upper frequency bound and , within , in terms of maximum and minimum degree of by the distance labeling and , respectively, for some order where are distinct prime and is any positive integer.