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...

Given an abelian group A, a graph G = (V, E) is said to have a distance two magic labeling in A if there exists a labeling l : E(G) → A − {0} such that the induced vertex labeling l∗ : V (G) → A defined by l∗(v) = ∑ e∈E(v) l(e) is a constant map, where E(v) = {e ∈ E(G) : d(v, e) < 2}. The set of all h ∈ Z+ for which G has a distance two magic labeling in Zh is called the distance two magic spec...

The concept of fuzzy magic labeling is introduced.Fuzzy magic labeling for some graphs like path, cycle and star graph are defined. It is proved that, every fuzzy magic graph is a fuzzy labeling graph, but the converse is not true. And we show that the removal of a fuzzy bridge from a fuzzy magic graph G, such that G* is a cycle with odd number of nodes is a fuzzy magic graph.And also some prop...

ON SUPER EDGE-MAGIC TOTAL LABELING OF REFLEXIVE W-TREES Muhammad Imran, Mehar Ali Malik, M. Yasir Hayat Malik Department of Mathematics, School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Islamabad, Pakistan. E-mail: {imrandhab, alies.camp, yasirmalikawan}@gmail.com Mathematics Subject Classification: 05C78 ABSTRACT. Kotzig and Rosa [17] defined a magic lab...

Z k-magic labelings of fans and wheels with magic-value zero Abstract Let A be a non-trivial abelian group and A * = A − {0}. A graph is A-magic if there exists an edge labeling using elements of A * which induces a constant vertex labeling of the graph. For fan graphs F n and wheel graphs W n , we determine the sets of numbers k ∈ N, where F n and W n have Z k-magic labelings with magic-value 0.

An H-magic labeling in a 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, ΣνεV(H) f(v) +  ΣeεE(H) f(e) is constant. f is said to be H-E-super magic if f(E(G)) = {1, 2, · · · , q}. A family of subgraphs H1,H2, · · · ,Hh of G is a mixed cycle-decomposition of G if every subgraph Hi is isomorphic to some cycle Ck, for k ≥ ...

An H-magic labeling in a 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, ∑νεV (H) f(v) + ∑νεE (H) f(e) is constant. f is said to be H-E-super magic if f(E(G)) = {1, 2, · · · , q}. A family of subgraphs H1,H2, · · · ,Hh of G is a mixed cycle-decomposition of G if every subgraph Hi is isomorphic to some cycle Ck, for k ≥...

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...

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. 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...