H-E-Super magic decomposition of graphs - S.P. Subbiah; J. Pandimadevi (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2014)
An H-magic labeling in an H-decomposable graph G is a bijection f:V(G) U E(G) –> 1,2, … ,p+q such that for every copy H in the decomposition, _vV(H) f(v)+_eE(H) f(e) is constant. The function f is said to be H-E-super magic if f(E(G)) = 1,2, … ,q. In this paper, we study some basic properties of m-factor-E-super magic labelingand we provide a necessary and sufficient condition for an even regular graph to be 2-factor-E-super magic decomposable. For this purpose, we use Petersen's theorem and magic squares.