New Labeling Algorithm on Various Classes of Graphs with Applications

In order to develop an algorithm, computer theories are essential and often used in a mathematical sequence. Most of them without sufficient mathematics are difficult to understand. A mathematical algorithm is, therefore, a better guide to confirm whether or not a software is correct. This implies that a mathematical knowledge-based algorithm is of great concern. Let S={r1, r2, ...rφ(n)} be a set of all co-prime residues of a positive integer n. An integer is termed as totient if the sum of co-prime residues of n is 2
^k
n, k ≥ 1. A graph G with V and E be the set of vertices and edges of G respectively, then G is said to be a totient graph if there exists a one-one function h:V→ N, whose induced function h
^*
:E→ N, defined by f
^*
(ab)=f(a)f(b) assigns a totient number for each edge of G. In this piece of work, we propose new labeling algorithms for several classes of graphs.