Harmonic Mean Cordial labeling in the scenario of duplicating graph elements

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. A Graph G is called Harmonic Mean Cordial graph if it admits Harmonic Mean Cordial labeling. In this article, we have discussed Harmonic Mean Cordial labeling In The Scenario of Duplicating Graph Elements.