Union of Distance Magic Graphs

Abstract

A distance magic labeling of a graph G = (V,E) with |V | = n is a bijection ℓ from V to the set {1, . . . , n} such that the weight w(x) = ∑y∈NG(x) ℓ(y) of every vertex x ∈ V is equal to the same element μ, called the magic constant. In this paper, we study unions of distance magic graphs as well as some properties of such graphs.

Keywords

• distance magic labeling
• magic constant
• sigma labeling
• graph labeling
• union of graphs
• lexicographic product
• direct product
• kronecker product
• kotzig array
• 05c76
• 05c78