On Group Distance Graph Evaluation

Abstract

Graph help us for building the interconnection network that are required by systems. The unique graph labeling help us to ensure the functionality of these networks.In this research we have discuss the labeling of certain graphs and how we develope the labeling pattern for these graphs.We have used modulo group combinatorial techniques to find out the labeling schemes.By using elements from modulo group we have define group distance and distance magic labeling. We have calculate the weight of vertices and magic constant of graphs by finding the labeling of direct product of prism graph and cycle graph Pn × C4 under modulo group Z8n and Pn × Cm under modulo group Zm × Z2n ∀ n = 3 and m =≥ 4