HARMONIC MEAN CORDIAL LABELING IN THE SCENARIO OF DUPLICATING GRAPH ELEMENTS

HARMONIC MEAN CORDIAL LABELING IN THE SCENARIO OF DUPLICATING GRAPH ELEMENTS

H. Gandhi, J. Parejiya, M. M. Jariya

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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.

Keywords

Harmonic Mean Cordial Labeling, Vertex Duplication, Edge Duplication, Cycle.