Balanced Traffic Splitting in Communication Network Using Parity Sum Cordial Labelling of Graphs

Abstract

Labeling of graph is the assignment of integers to the elements of a graph such as vertices, edges or both. This process gives an easiest way of modelling real world networks. Different types of labeling are available in the literature. Parity sum cordial labeling is a new graph labeling that we defined in this paper. Let G₁ be a (p, q) graph. Let f_v be an injective map from vertex set of G₁ to {1, 2, .....p}. For each edge {x, y} assign the label f_v(x) + f_v(y). f_v is named a parity sum cordial labeling (PSC-labeling), if f_v is a bijective map and |e(0) - e(1)| <=1, where e(0) and e(1) denote the number of edges labelled with even numbers and odd numbers respectively. A graph which follows partiy sum cordial labeling is a parity sum cordial graph (PSC graph). Also we investigate the PSC-labeling behaiour of path graph, cycle graph, comb graph, complete graph and illustrated Balanced Traffic Splitting in communication networ, using PSC Labeling. With this routers or load balancers can direct traffic based on parity and maintain equal load on both ports. It helps to avoid server overload.