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...

A (p,q) graph G is total edge-magic if there exits a bijection f: Vu E ~ {1.2,. .. ,p+q} such that for each e=(u,v) in E, we have feu) + fee) + f(v) as a constant. For a graph G, denote M(G) the set of all total edge-magic labelings. The magic strength of G is the minimum of all constants among all labelings in M(G), and denoted by emt(G). The maximum of all constants among M(G) is called the m...

Acharya and Hegde have introduced the notion of strongly k-indexable graphs: A (p, q)-graph G is said to be strongly k-indexable if its vertices can be assigned distinct integers 0, 1, 2, ..., p − 1 so that the values of the edges, obtained as the sums of the numbers assigned to their end vertices can be arranged as an arithmetic progression k, k+ 1, k + 2, ..., k + (q − 1). Such an assignment ...

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 distance magic labeling of a graph G = (V, E) of order n is a bijection l : V → {1, 2, . . . , n} with the property that there is a positive integer k (called magic constant) such that w(x) = k for every x ∈ V . If a graph G admits a distance magic labeling, then we say that G is a distance magic graph. In the case of non-regular graph G, the problem of determining whether there is a distance...

A simple graph G = (V,E) admits an H-covering if every edge in E belongs at least to one subgraph of G isomorphic to a given graph H . Then the graph G admitting an H-covering is (a, d)-H-antimagic if there exists a bijection f : V ∪ E → {1, 2, . . . , |V | + |E|} such that, for all subgraphs H ′ of G isomorphic to H , the H ′-weights, wtf(H ′) = ∑ v∈V (H′) f(v) + ∑ e∈E(H′) f(e), form an arithm...

A total labeling of a graph with v vertices and e edges is defined as a one-to-one map taking the vertices and edges onto the integers 1, 2, · · · , v+e. Such a labeling is vertex magic if the sum of the label on a vertex and the labels on its incident edges is a constant independent of the choice of vertex, and edge magic if the sum of an edge label and the labels of the endpoints of the edge ...

The study of graph labeling has focussed on finding classes of graphs which admits a particular type of labeling. In this paper we consider a particular class of graph which admits a vertex magic total labeling. The class we considered here is the class of complete graphs, Kn . A vertex magic labeling of a graph is a bijection which maps the vertices V and edges E to the integers from 1, 2, 3, ...