H-E-Super magic decomposition of graphs

An H-magic labeling in an H-decomposable graph G is a bijection f : V (G)∪E(G) → {1, 2, . . . , p + q} such that for every copy H in the decomposition, ∑ v∈V (H) f (v) + � e∈E(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 labeling and 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.