# On k-Super Mean Graphs

**Journal**: International Journal of Scientific Engineering and Research (IJSER) (Vol.5, No. 8)

**Publication Date**: 2017-08-05

**Authors** : M. Tamilselvi; S. Ilakkiya;

**Page** : 102-107

**Keywords** : k - super mean labeling; k - super mean graph; (nQ_3v_1v_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;

### 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.

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