Even-Odd Harmonious Labeling of Certain Family of Cyclic Graphs

Abstract

An even-odd harmonious labeling of a graph G with p vertices and q edges is a process of assigning odd numbers 1,3,5,...,2q 1 to the vertices through a 1-1 computing function f and even numbers 0, 2, 4,..., 2( p 1) to the edges through a bijective computing function f * with the condition that f *(e  uv)  ( f (u)  f (v))(mod 2q) where u and v are the vertices of G . This type of labelled graph is called as even-odd harmonious graph.