A (p; q)-graph G is edge-magic if there exists a bijective function f : V (G)∪E(G) → {1; 2; : : : ; p + q} such that f(u) + f(v) + f(uv) = k is a constant, called the valence of f, for any edge uv of G. Moreover, G is said to be super edge-magic if f(V (G)) = {1; 2; : : : ; p}. In this paper, we present some necessary conditions for a graph to be super edge-magic. By means of these, we study the super edge-magic properties of certain classes of graphs. We also exhibit the relationships between super edge-magic labelings and other well-studied classes of labelings. In particular, we prove that every super edge-magic (p; q)-graph is harmonious and sequential (for a tree or q ¿ p) as well as it is cordial, and sometimes graceful. Finally, we provide a closed formula for the number of super edge-magic graphs.

No abstract

In this paper, a complete characterization of the (super) edge-magic linear forests with two components is provided. In the process of establishing this characterization, the super edge-magic, harmonious, sequential and felicitous properties of certain 2-regular graphs are investigated, and several results on super edge-magic and felicitous labelings of unions of cycles and paths are presented. These labelings resolve one conjecture on harmonious graphs as a corollary, and make headway towards the resolution of others. They also provide the basis for some new conjectures (and a weaker form of an old one) on labelings of 2-regular graphs.

No abstract

We modify a standard Freshman physics experiment with the aim to produce high density plots of two-dimensional electric potentials versus position. To achieve this we connect a voltage probe to a rotary motion sensor and a computer interface so that it becomes possible to sample and record the potential at high rates through horizontal and vertical transects of the conductive paper. We perform some data filtering, and then illustrate the method with the electric dipole.