H-V-super magic decomposition of complete bipartite graphs

Abstract

An H-magic labeling in a H-decomposable graph G is a bi-jection f: V (G){n-ary union}E(G) → {1, 2, . . . , p + q} such that for every copy H in the decomposition, ∑ vεV (H) f(v) +∑ eεE(H) f(e) is constant. f is said to be H-V -super magic if f(V (G)) = {1, 2, . . . , p}. In this paper, we prove that complete bipartite graphs K n,n are H-V -super magic decomposable where H ≅= K 1,n with n ≥ 1.