D-Magic Labelings Of The Folded N-Cube

Let G be a finite undirected simple connected graph with vertex set V(G), distance function partial derivative and diameter d. Let D subset of {0, 1, ..., d} be a set of distances. A bijection l : V(G) -> {1, 2, ..., vertical bar V(G)vertical bar} is called a D-magic labeling of G if there exists a constant k such that Sigma(x is an element of ND(v)) l(x) = k for any vertex v is an element of V(G), where N-D(v) = {x is an element of V(G) : partial derivative(x, v) is an element of D}. We say Ghas a D-magic labeling if G admits a D-magic labeling. In this paper, we show that the folded n-cube has a {1}-magic labeling (resp. a {0, 1}-magic labeling) if and only if n equivalent to 0(mod 4) (resp. n equivalent to 3(mod 4)). (C) 2021 Elsevier B.V. All rights reserved.