Harmonic Mean Cordial Labeling of Join 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 | v_f (i)- v_f (j)|≤1 and | e_f (i)-e_f (j)|≤ 1 for any i,j∈{1,2}, where v_f (x) and e_f (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 C_n∨W_m and K_n∨W_m.