Motivated by a conjecture of Liang [Y.-C. Liang. Anti-magic labeling of graphs. PhD thesis, National Sun Yat-sen University, 2013.], we introduce a restricted path packing problem in bipartite graphs that we call a V-free 2-matching. We verify the conjecture through a weakening of the hypergraph matching problem. We close the paper by showing that it is NP-complete to decide whether one of the ...

A vertex magic total (VMT) labeling of a graph G = (V,E) is a bijection from the set of vertices and edges to the set of integers defined by λ : V ∪E → {1, 2, . . . , |V | + |E|} so that for every x ∈ V , w(x) = λ(x)+ ∑ xy∈E λ(xy) = k, for some integer k. A VMT labeling is said to be a super VMT labeling if the vertices are labeled with the smallest possible integers, 1, 2, . . . , |V |. In thi...

An edge-magic total labeling on G is a one-to-one map λ from V (G) ∪ E(G) onto the integers 1, 2, . . . , |V (G) ∪ E(G)| with the property that, given any edge (x, y), λ(x) + λ(x, y) + λ(y) = k for some constant k. The labeling is strong if all the smallest labels are assigned to the vertices. Enomoto et al. proved that a graph admitting a strong labeling can have at most 2|V (G)| − 3 edges. In...

Let Γ=(V,E) be a graph of order n. A closed distance magic labeling Γ is bijection ℓ:V→{1,2,…,n} for which there exists positive integer r such that ∑x∈N[u]ℓ(x)=r all vertices u∈V, where N[u] the neighborhood u. said to if it admits labeling. In this paper, we classify connected circulants with valency at most 5, is, Cayley graphs Cay(Zn;S) |S|≤5, S=−S, 0∉S and S generates Zn.

We define a semi-magic square to be a square matrix whose entries are nonnegative integers and whose rows and columns (that is, lines) sum up to the same number. A magic square is a semimagic square whose main diagonals also add up to the line sum. A symmetric magic square is a magic square which is a symmetric matrix. A pandiagonal magic square is a semi-magic square whose diagonals parallel t...

Magic Lounge is a virtual meeting application which will integrate a number of technologies most of which are already known, such as www and video conferencing. In addition, Magic Lounge will integrate the innovations necessary to achieve the envisioned Magic Lounge functionality as described in [Dybkjær and Bernsen 1998]. Figure 1 outlines the physical Magic Lounge environment, i.e. how users ...

introduction: in radiotherapy, methods of treatment planning are becoming increasingly more complicated. this requires verification of the doses delivered to increasingly smaller and more precise regions. radiotherapy techniques are continuously employing smaller and smaller field sizes to deliver tighter radiation doses with higher therapeutic ratios, generating interest among researchers to p...

Magic rectangles are well-known for its very interesting and entertaining combinatorics. In a magic rectangle, the numbers 1 to mn are arranged in an array of m rows and n columns so that each row adds to the same total M and each column to the same total N . In the present paper we provide a new systematic method for constructing any even by even magic rectangle. The method proposed is extreme...