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...

Let G be a finite graph with p vertices and q edges. A vertex magic total labelling is a bijection from the union of the vertex set and the edge set to the consecutive integers 1, 2, 3, . . . , p + q with the property that for every u in the vertex set, the sum of the label of u and the label of the edges incident with u is equal to k for some constant k. Such a labelling is E-super, if the lab...

This work presents a Boolean satisfiability (SAT) encoding for a special problem from combinatorial optimization. In the last years much progress has been made in the optimization of practical SAT solvers (see the SAT competition [5]). This has made SAT encodings for combinatorial problems highly attractive. In this work we propose an encoding for the combinatorial problem Magic Labeling which ...

SUPER MAGIC AND ANTIMAGIC LABELINGS OF DISJOINT UNION OF PLANE GRAPHS Ali Ahmad, Martin Bača, Marcela Lascsáková, Andrea Semaničová-Feňovčíková 2,3 College of computer and information system, Jazan University, Jazan, Saudi Arabia Department of Appl. Mathematics and Informatics, Technical University, Košice, Slovak Republic Abdus Salam School of Mathematical Sciences, G. C. University, Lahore, P...

Let G = (V,E) be a finite (non-empty) graph, where V and E are the sets of vertices and edges of G. An edge magic total labeling is a bijection α from V ∪E to the integers 1,2, . . . , n+e, with the property that for every xy ∈E, α(x)+α(y)+α(xy)= k, for some constant k. Such a labeling is called an a-vertex consecutive edge magic total labeling if α(V )= {a + 1, . . . , a + n} and a b-edge cons...

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...