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 b...

Let G = (V,E) be a graph of order n. A bijection f : V → {1, 2, . . . , n} is called a distance magic labeling of G if there exists a positive integer μ such that ∑ u∈N(v) f(u) = μ for all v ∈ V, where N(v) is the open neighborhood of v. The constant μ is called the magic constant of the labeling f. Any graph which admits a distance magic labeling is called a distance magic graph. The bijection...

Let G be a finite graph with p vertices and q edges. A vertex magic total labeling is a bijection f from     G E G V  to the consecutive integers 1, 2, ..., p+q with the property that for every   G V u ,       k uv f u f u N v     for some constant k. Such a labeling is E-super if     q G E f , , 2 , 1 :   . A graph G is called E-super vertex magic if it admits an E-supe...

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.

Let G be a graph with vertex set V and edge set E , and let A be an abelian group. A labeling f : V → A induces an edge labeling f ∗ : E → A defined by f (xy) = f (x) + f (y). For i ∈ A, let v f (i) = card{v ∈ V : f (v) = i} and e f (i) = card{e ∈ E : f (e) = i}. A labeling f is said to be A-friendly if |v f (i)−v f ( j)| ≤ 1 for all (i, j) ∈ A× A, and A-cordial if we also have |e f (i) − e f (...

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...

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) = ∑ u∈N(v) l(uv) is a constant map. For a given graph G, the set of all k ∈ Z+ 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 trees whose diamet...

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 kEN, a graph G = (V, E) is said to be ;:z k-magic if there exists a labeling Z: E( G) --+ ;:z k {OJ such that the induced vertex set labeling Z+: V (G) --+ ;:z k defined by Z+(v) = L Z(uv) uvEE(G) is a constant map. For a given graph G, the set of all kEN for which G is ;:z k-magic is called the integer-magic spectrum of G and is denoted by IM(G). In this paper we will consider the func...