For any h ∈ IN , a graph G = (V, E) is said to be h-magic if there exists a labeling l : E(G) −→ ZZ h − {0} such that the induced vertex set labeling l : V (G) −→ ZZ h defined by l(v) = ∑ uv∈E(G) l(uv) is a constant map. For a given graph G, the set of all h ∈ ZZ + for which G is h-magic is called the integer-magic spectrum of G and is denoted by IM(G). The concept of integer-magic spectrum of ...

For any h ∈ Z, 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 set labeling l : V (G) → Zh defined by l(v) = ∑ uv∈E(G) l(uv) is a constant map. For a given graph G, the set of all h ∈ Z+ for which G is h-magic is called the integermagic spectrum of G and is denoted by IM (G). In this paper, we will determine the integer-magic sp...

For any abelian group A, a graph G = (V, E) is said to be A-magic if there exists a labeling l : E(G) −→ A − {0} such that the induced vertex set labeling l : V (G) −→ A defined by l(v) = ∑ { l(uv) | uv ∈ E(G) } is a constant map. In this paper we will consider the Klein-four group V4 = ZZ 2 ⊕ ZZ 2 and investigate graphs that are V4-magic.

Let A be a non-trivial Abelian group. We call a graph G = (V, E) A-magic if there exists a labeling f : E → A∗ such that the induced vertex set labeling f : V → A, defined by f(v) = ∑ uv∈E f(uv) is a constant map. In this paper, we show that Kk1,k2,...,kn (ki ≥ 2) is A-magic, for all A where |A| ≥ 3.

A vertex-magic group edge labeling of a graph G(V,E) with |E| = n is an injection from E to an abelian group Γ of order n such that the sum of labels of all incident edges of every vertex x ∈ V is equal to the same element μ ∈ Γ. We completely characterize all Cartesian products Cn Cm that admit a vertex-magic group edge labeling by Z2nm, as well as provide labelings by a few other finite abeli...

A group distance magic labeling of a graph G(V, E) with |V | = n is an injection from V to an abelian group Γ of order n such that the sum of labels of all neighbors of every vertex x ∈ V is equal to the same element μ ∈ Γ. We completely characterize all Cartesian products Ck Cm that admit a group distance magic labeling by Zkm.

Let A be an abelian group. An A-magic of a graph G = (V, E) is a labeling f : E(G) → A\{0} such that the sum of the labels of the edges incident with u ∈ V is a constant, where 0 is the identity element of the group A. In this paper we prove Z3-magic labeling for the class of even cycles, Bistar, ladder, biregular graphs and for a certain class of Cayley digraphs. Mathematics Subject Classifica...

An anti-magic labeling of a finite simple undirected graph with p vertices and q edges is a bijection from the set of edges to the integers {1, ..., q} such that all p vertex sums are pairwise distinct, where the vertex sum on a vertex is the sum of labels of all edges incident to such vertex. A graph is called anti-magic if it has an anti-magic labeling. Hartsfield and Ringel [3] conjectured t...