Zero-Sum Magic Graphs And Their Null Sets

For any h ∈ N, a graph G = (V, E) is said to be h-magic if there exists a labeling l : E(G) → Zh − {0} such that the induced vertex labeling l+ : V (G) → Zh defined by l+ (v) = uv∈E(G) l(uv) is a constant map. When this constant is 0 we call G a zero-sum h-magic graph. The null set of G is the set of all natural numbers h ∈ N for which G admits a zero-sum h-magic labeling. A graph G is said to be uniformly null if every magic labeling of G induces zero sum. In this paper we will identify the null sets of the generalized theta graphs and will introduce a class of uniformly null magic graphs.

• Type: Journal
• Year: 2007
• Where: ARSCOM
• Authors: Ebrahim Salehi
• Keywords: ARSCOM 2007, Constant Map, Zero-sum H-magic Graph, Zero-sum H-magic Labeling