Let G be a subdivision of a ladder graph. In this paper we study magic evaluation with type (1, 1, 1) for a given any general ladder graph G. We prove that subdivided ladder admits magic evaluation having type (1, 1, 1). We also prove such a subdivision admits consecutive magic evaluation having type (1, 1, 0). AMS (MOS) Subject Classification Codes: 05C78

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 set of integers {1, 2, ..., q} such that the vertex sums are pairwise distinct, where the vertex sum at vertex u is the sum of labels of all edges incident to such vertex. A graph is called anti-magic if it admits an antimagic labeling. Hartsfield and Ringel conject...

where E(v) is the set of edges that have v as an end-point. The total labelling λ of G is vertex-magic if every vertex has the same weight, and the graph G is vertexmagic if a vertex-magic total labelling of G exists. Magic labellings of graphs were introduced by Sedlácěk [5] in 1963, and vertex-magic total labellings first appeared in 2002 in [4]. For a dynamic survey of various forms of graph...

An H-magic labeling in an H-decomposable graph G is a bijection f : V (G)∪E(G)→ {1, 2, . . . , p+ q} such that for every copy H in the decomposition, ∑ v∈V (H) f(v)+ ∑ e∈E(H) f(e) is constant. The function f is said to be H-E-super magic if f(E(G)) = {1, 2, . . . , q}. In this paper, we study some basic properties of m-factor-E-super magic labeling and we provide a necessary and sufficient cond...

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...

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...

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 ...

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...

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.

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...