On k-Super Mean Labeling of Some Graphs

Dr. M. Tamilselvi, K. Synthiya

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 L_n?K_1, S(T_n), S(T_(n )? k_1), (P_n:C_4), [P_n:C_6^2].

Keywords: Keyword: k - super mean labeling, k - super mean graph, L_n?K_1, S(T_n), S(T_(n )? k_1), (P_n:C_4), [P_n:C_6^2].