HARMONIC MEAN CORDIAL LABELING OF SOME WELL KNOWN GRAPHS

HARMONIC MEAN CORDIAL LABELING OF SOME WELL KNOWN GRAPHS

J. Parejiya, P. T. Lalchandani, D. B. Jani, S. Mundadiya

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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 and ⌊x⌋ 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 discussed Harmonic Mean Cordial labeling of splitting graphs graph of some well known graphs.

Keywords

Harmonic Mean Cordial, Splitting graph, Corona Product, Path graph, Star Graph, Bistar Graph.