where E(v) is the set of edges that have v as an end-point. The total labelling λ of G is vertex-magic if every vertex has the same weight, and the graph G is vertexmagic if a vertex-magic total labelling of G exists. Magic labellings of graphs were introduced by Sedlácěk [5] in 1963, and vertex-magic total labellings first appeared in 2002 in [4]. For a dynamic survey of various forms of graph...

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...

This paper describes techniques in computational creativity, blending mathematical modeling and psychological insight, to generate new magic tricks. The details of an explicit computational framework capable of creating new magic tricks are summarized, and evaluated against a range of contemporary theories about what constitutes a creative system. To allow further development of the proposed sy...

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...

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...

A graph is magic if the edges can be labeled with nonnegative real numbers such that (i) different edges have distinct labels, and (ii) the sum of the labels of edges incident to each vertex is the same. Regular magic graphs are characterized herein by the nonappearance of certain bipartite subgraphs. This implies that line connectivity is a crucial property for characterizing regular magic gra...

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...

background: accurate small radiation field dosimetry is essential in modern radiotherapy techniques such as stereotactic radiosurgery (srs) and intensity modulated radiotherapy (imrt). precise measurement of dosimetric parameters such as beam profile, percentage depth doses and output factor of these beams are complicated due to the electron disequilibrium and the steep dose gradients. in the p...

A magic square of order n consists of the numbers 1 to n placed such that the sum of each row, column and principal diagonal equals the magic sum n(n +1)/2. In addition, an odd ordered magic square is associative or self-complementary if diagonally opposite elements have the same sum (n +1)/2. The magic square is said to be regular Greco-Latin if it can be decomposed as a sum of a pair of Latin...

Physics interpretation of the " magic " baseline, L magic , that can play important role in future oscillation experiments is given. The " magic " baseline coincides with the refraction length, l 0. The latter, in turn, approximately equals the oscillation length in matter at high energies. Therefore at the baseline L = l 0 the oscillation phase is 2π, and consequently, the " solar " amplitude ...