Harmonic Mean Cordial labeling of some graphs

Abstract

All the graphs considered in this article are simple and undirected. Let G = (V(G), E(G)) be a simple undirected Graph. A function f : V (G) ? {1, 2} is called Harmonic Mean Cordial if the induced function f*: E(G) ? {1, 2} defined by f* (uv) = [2f(u)f(v)/f(u)+f(v)] satisfies the condition |vf (i) ? vf (j)| ? 1 and |ef (i) ? ef (j)| ? 1 for any i, j ? {1, 2}, where vf (x) and ef (x) denotes the number of vertices and number of edges with label x respectively and bxc denotes the greatest integer less than or equals to x. A Graph G is called Harmonic Mean Cordial graph if it admits Harmonic Mean Cordial labeling. In this article, we have provided some graphs which are not Harmonic Mean Cordial and also we have provided some graphs which are Harmonic Mean Cordial.