Lucas Mean Labeling for Some Graphs - A. Ponmoni; S. Navaneetha Krishnan; A. Nagarajan (International Journal of Mathematics And its Applications, 2018)
A function f is called Lucas mean labeling of graph G if f:V(G)→{0,1,2,… ,L_p+q} is injective and the induced function f:E(G)→{L_1,L_2,… ,L_q} defined as \[ f^*(e=uv)={arrayll f(u)+f(v)2& if f(u)+f(v) is even f(u)+f(v)+12& if f(u)+f(v) is oddarray . \] is bijective. A graph which admits Lucas mean labeling is called Lucas mean graph. In this paper, we proved for some graphs such as path P_n, Twigs T_n, P_nK_1, the graph obtained by the subdivision of the edges of the path P_n in comb P_nK_1, (C_3K_1,n), C_3, K_1,n , C_3^*, K_1,n , (3,n) kite graph, B_m,n, K_1,n,nK_1,m,m are Lucas mean graph.