Star-Supermagic Decompositions of the Complete Bipartite Graph Minus a One-Factor

Abstract

Let G be a graph and let H be a subgraph of G. Assume that G has an H-decomposition T={H1,H2,.,Ht} such that Hi≅H for all 1≤i≤t. An H-supermagic decomposition of G is a bijection f:V(G)∪E(G)→1,2,.,VG+EG such that ∑vϵV(Hi)f(v)+∑eϵE(Hi)f(e) is a constant k for each Hi in the decomposition T and fVG=1,2,.,VG. If G admits an H-supermagic decomposition, then G is called H-supermagic decomposable. In this paper, we give necessary and sufficient conditions for the existence of K1,n-1-supermagic decomposition of the complete bipartite graph Kn,n minus a one-factor. © 2017 Tanawat Wichianpaisarn and Uthoomporn Mato.