A Study of Cordial Labeling of Friendly Index Related Graphs: Exploring Various Labeling Techniques in Graph Theory

Abstract

One of the most interesting problems in the area of Graph Theory is that of labeling of graphs. Alabeling or valuation or numbering of a simple graph G is a one-to-one mapping from its vertex set (edgeset) into a set of non-negative integers which induces an assignment of labels to the edges (vertices) ofG. Labeled graphs serve as useful models for a broad range of applications. They are useful in manycoding theory problems, including the design of good radar type codes. Synch-set codes, missileguidance codes and convolution codes with optimal non – standard encodings of integers. Labeledgraphs have also been applied in determining ambiguities in X – ray crystallographic analysis, anddesigning a communication network addressing system in determining optional circuit layouts and radioastronomy problems. Apart from the graceful labeling, some other labeling was also defined anddeveloped. Graham and Sloane introduced harmonious graphs. Some of the other known labelings arePrime labeling, Arithmetic labeling, Edge graceful labeling, Felicitious labeling, Antimagic labeling,Cordial labeling, Prime cordial labeling, Edge cordial labeling, Ek – cordial labeling, Difference cordiallabeling, Friendly labeling, Divisor cordial labeling, Skolem graceful labeling, Product cordial labeling.