## M MODULO N GRACEFUL LABELING OF PATH UNION AND JOIN SUM OF COMPLETE BIPARTITE GRAPHS WITH ITS ALGORITHMS

## M MODULO N GRACEFUL LABELING OF PATH UNION AND JOIN SUM OF COMPLETE BIPARTITE GRAPHS WITH ITS ALGORITHMS

*C. Velmurugan, V. Ramachandran*

[**PDF**]

## Abstract

A graceful labeling of a graph G(p; q) is an injective assignment of labels from the set f0; 1; :::; qg to the vertices of G such that when each edge of G has been assigned a label de ned by the absolute di erence of its end-vertices, the resulting edge labels are distinct. In this paper we used the new labeling technique known as M modulo N graceful labeling and prove that path union of complete bipartite graphs and join sum of complete bipartite graphs are M modulo N graceful labeling. We also give a C + + program for nding M modulo N graceful labeling on above said graphs.

## Keywords

Complete bipartite graph, Join sum of complete bipartite, Path union of com- plete bipartite graphs, One modulo N graceful labeling, M modulo N graceful labeling.