A Novel Labeling Algorithm on Several Classes of Graphs

Abstract

A positive integer n is called super totient if the residues of n which are prime to n can be partitioned into two disjoint subsets of equal sums. Let G be a given graph with V, the set of vertices and E is the set of its edges. An injective function g defined on V into subset of integers will be termed as super totient labeling of the graph G, if the function g ∗ : E → N defined by g ∗ (xy) = g(x)g(y) assigns a super totient number for all edges xy ∈ E, where x, y ∈ V. A graph admits this labeling is called a super totient graph. In the current manuscript, the authors investigate a novel labeling algorithm, called super totient labeling, for several classes of graphs such as friendship graphs, wheel graphs, complete graphs and complete bipartite graphs.