An edge-magic total labeling of a graph G is a one-toone map λ from V (G) ∪ E(G) onto the integers {1, 2, · · · , |V (G) ∪ E(G)|} with the property that, there is an integer constant c such that λ(x) + λ(x, y) + λ(y) = c for any (x, y) ∈ E(G). If λ(V (G)) = {1, 2, · · · , |V (G|} then edge-magic total labeling is called super edgemagic total labeling. In this paper we formulate super edge-magic...

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 ...

An edge-magic total labeling of a graph G is a one-toone map λ from V (G) ∪ E(G) onto the integers {1, 2, · · · , |V (G) ∪ E(G)|} with the property that, there is an integer constant c such that λ(x) + λ(x, y) + λ(y) = c for any (x, y) ∈ E(G). If λ(V (G)) = {1, 2, · · · , |V (G|} then edge-magic total labeling is called super edgemagic total labeling. In this paper, we formulate super edge-magi...

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 of order p and size q is edge-magic if there is a bijective function f : V (G) ∪ E(G) −→ {i} i=1 such that f(x) + f(xy) + f(y) = k, for all xy ∈ E(G). The function f is an edge-magic labeling of G and the sum k is called either the magic sum, the valence or the weight of f . Furthermore, if f(V (G)) = {i}pi=1 then f is a super edge-magic labeling of G. In this paper we study the valen...

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...

A graph G admits an H-covering if every edge of belongs to a subgraph isomorphic given H. is said be H-magic there exists bijection f:V(G)∪E(G)→{1,2,…,|V(G)|+|E(G)|} such that wf(H′)=∑v∈V(H′)f(v)+∑e∈E(H′)f(e) constant, for H′ In particular, H-supermagic f(V(G))={1,2,…,|V(G)|}. When H complete K2, H-(super)magic labeling edge-(super)magic labeling. Suppose F-covering and two graphs F We define (...

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...