An application on edge irregular reflexive labeling for $ m^t $-graph of cycle graph

Abstract

Graph labeling is an increasingly popular problem in graph theory. A mapping converts a collection of graph components into a set of integers known as labels. Graph labeling techniques typically label edges with positive integers, vertices with even numbers, and edge weights with consecutive numbers, known as edge irregular reflexive total labeling. This is achieved by utilizing the reflexive edge irregularity strength of the graphical structure. The edge calculates the exact values of the reflexive edge irregularity strength irregular reflexive labeling for the $ m^t $-graph of cycle graph $ mC_n $ on $ t = 1 $ with $ n \geq 3 $ and $ m \geq 4 $. The maximum number of assignments assigned to each individual in a communication network, as well as providing a secure communication channel to ensure the unique identification of each employee, are potential applications for this problem.

Keywords

• reflexive edge irregularity strength
• $ m^t $-graphs
• edge irregular reflexive total labeling