An edge magic total labeling of a graph G(V,E) with p vertices and q edges is a bijection f from the set of vertices and edges to such that for every edge uv in E, f(u) + f(uv) + f(v) is a constant k. If there exist two constants k1 and k2 such that the above sum is either k1 or k2, it is said to be an edge bimagic total labeling. A total edge magic (edge bimagic) graph is called a super edge m...

For a positive integer k, a graph G (V, E) is £k-magic if there exists a function, namely, a labeling, I : E(G) -+ £k such that the induced vertex set labeling [+ : V(G) £k, where [+(v) is the sum of the labels of the edges incident with a vertex v is a constant map. The set of all positive integer k such that G is k-magic is denoted by IM(G). We call this set the integer-magic spectrum of G. I...

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 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 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...

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...