A (p,q) graph G is called super edge-magic if there exists a bijective function f from V (G) ∪ E(G) to {1, 2,. .. , p + q} such that f (x) + f (xy) + f (y) is a constant k for every edge xy of G and f (V (G)) = {1, 2,. .. , p}. Furthermore, the super edge-magic deficiency of a graph G is either the minimum nonnegative integer n such that G ∪ nK 1 is super edge-magic or +∞ if there exists no suc...

Magic rectangles are well-known for their very interesting and entertaining combinatorics. Such magic rectangles have also been used in designing experiments. In a magic rectangle, the integers 1 to pq are arranged in an array of p rows and q columns so that each row adds to the same total P and each column to the same total Q. In the present paper we provide a systematic method for constructin...

The security of any cryptosystems is based on the way in which it produces different ciphertext for the same plaintext. Normally, various block cipher modes viz., CBC, OFC, etc., are used in producing different ciphertext for the same plaintext but it is a time consuming process. Instead of using block cipher, a different encoding method for the plaintext is proposed in this paper using magic r...

Let G = (V,E) be a graph of order n. A bijection f : V → {1, 2, . . . , n} is called a distance magic labeling of G if there exists a positive integer μ such that ∑ u∈N(v) f(u) = μ for all v ∈ V, where N(v) is the open neighborhood of v. The constant μ is called the magic constant of the labeling f. Any graph which admits a distance magic labeling is called a distance magic graph. The bijection...

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...

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 one vertex is the sum of labels of all edges incident to such vertex. A graph is called anti-magic if it admits an anti-magic labeling. Hartsfield and Ringel c...

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...

A magic square is an n × n array of distinct positive integers whose sum along any row, column, or main diagonal is the same number. We compute the number of such squares for n = 4, as a function of either the magic sum or an upper bound on the entries. The previous record for both functions was the n = 3 case. Our methods are based on inside-out polytopes, i.e., the combination of hyperplane a...

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 ...