Let G = (V,E) be a graph and Γ an abelian group, both of order n. A group distance magic labeling of G is a bijection : V → Γ for which there exists μ ∈ Γ such that ∑x∈N(v) (x) = μ for all v ∈ V, where N(v) is the neighborhood of v. Froncek [Australas. J. Combin. 55 (2013), 167–174] showed that the cartesian product Cm Cn, m,n ≥ 3 is a Zmn-distance magic graph if and only if mn is even. In this...

Gallian’s survey shows that there is a big variety of labelings of graphs. By means of (di)graphs products we can establish strong relations among some of them. Moreover, due to the freedom of one of the factors, we can also obtain enumerative results that provide lower bounds on the number of nonisomorphic labelings of a particular type. In this talk, we will focus in three of the (di)graphs p...

A graph G is said to be A-magic if there is a labeling l : E(G) −→ A − {0} such that for each vertex v, the sum of the labels of the edges incident with v are all equal to the same constant; that is, l+(v) = c for some fixed c ∈ A. In general, a graph G may admit more than one labeling to become A-magic; for example, if |A| > 2 and l : E(G) −→ A − {0} is a magic labeling of G with sum c, then l...

A (p, q)-graph G = (V, E) is said to be magic if there exists a bijection f : V ∪ E → {1, 2, 3, . . . , p + q} such that for all edges uv of G, f(u) + f(v) + f(uv) is a constant. The minimum of all constants say, m(G), where the minimum is taken over all such bijections of a magic graph G, is called the magic strength of G. In this paper we define the maximum of all constants say, M(G), analogo...

Let A be an abelian group. We call a graph G = (V,E) A–magic if there exists a labeling f : E(G) → A− {0} such that the induced vertex set labeling f+ : V (G) → A, defined by f+(v) = Σf(u, v) where the sum is over all (u, v) ∈ E(G), is a constant map. For four classical products, we examine the A–magic property of the resulting graph obtained from the product of two A–magic graphs.

A vertex magic total labeling on a graph with v vertices and e edges is a one to one map taking the vertices and edges onto the integers with the property that the sum of the label on the vertex and the labels of its incident edges is a constant, independent of the choice of the vertex. A graph with vertex magic total labeling with two constants or is called a vertex bimagic total labeling. The...

For any k ∈ N, a graph G = (V, E) is said to be Zk-magic if there exists a labeling l : E(G) → Zk − {0} such that the induced vertex set labeling l : V (G) → Zk defined by l(v) = ∑ uv∈E(G) l(uv) is a constant map. For a given graph G, the set of all k ∈ N for which G is Zk-magic is called the integer-magic spectrum of G and is denoted by IM(G). In this paper we will consider the functional exte...

Let G = (V, E) be a graph on n vertices. A bijection f : V → {1, 2, . . . , n} is called a distance magic labeling of G if there exists an integer k such that ∑ u∈N(v) f(u) = k for all v ∈ V , where N(v) is the set of all vertices adjacent to v. The constant k is the magic constant of f and any graph which admits a distance magic labeling is a distance magic graph. In this paper we solve some o...

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. 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 ∈ IN for which G admits a zero-sum h-magic labeling. In this pap...