On k-Super Mean Graphs

Dr. M. Tamilselvi, S. Ilakkiya

Abstract: Let G be a (p, q) graph and f: V(G)?{1, 2, 3, ?..p+q} be an injection. For each edge e=uv, let f*(e) = (f(u)+ f(v))/2 if f(u)+f(v) is even and f*(e) = (f(u)+ f(v) + 1)/2 if f(u) +f(v) is odd, then f is called super mean labeling if f(V)?{f*(e): e? E(G)={1, 2, 3, ?..p+q}. A graph that admits a super mean labeling is called super mean graph. Let G be a (p, q) graph and f: V(G)?{k, k+1, k+2,..p+q+ k- 1} be an injection. For each edge e=uv, let f*(e) = (f(u)+ f(v))/2 if f(u)+f(v) is even and f*(e) = (f(u)+ f(v) + 1)/2 if f(u)+f(v) is odd, then f is called k - super mean labeling if f(V)?{f*(e): e? E(G)}= { k, k+1, k+2, ?..p+q+k-1}. A graph that admits a k - super mean labeling is called k - super mean graph. In this paper, we investigate k-super mean labeling of (nQ_3, v_1, v_2 ), TP_n , S(P_m? P_n), (P_n A K_1) ?T_m, A(T_n ), C_n ?2P_(m ), TL_n?K_1.

Keywords: k - super mean labeling, k - super mean graph, (nQ_3,v_1,v_2 ),TP_n, S(P_m? P_n), (P_n A K_1) ?T_m, A(T_n ) ,C_n ?2P_m, TL_n?K_1