Let G=(V,E,F) be an embedding of a graph and a,b,c belong to {0,1}. A labeling type (a,b,c) is assignment labels from the set {1,2,...,a|V|+b|E|+c|F|} so that each vertex receives labels, edge b face c no label used more than once. If weight every s-sided face, defined as sum with vertices edges border equal some fixed constant w(s), then said face-magic. We investigate face-magic labelings all...

A (p, q)-graph G is called super 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) is a constant for each uv ∈ E(G) and f(V (G)) = {1, 2, . . . , p}. In this paper, we introduce the concept of strong super edgemagic labeling as a particular class of super edge-magic labelings ∗Supported by Slovak VEGA Grant 1/4005/07. †Supported i...

A 1-vertex-magic vertex labeling of a graph G(V,E) with p vertices is a bijection f from the vertex set V (G) to the integers 1, 2, . . . , p with the property that there is a constant k such that at any vertex x the sum ∑ f(x) taken over all neighbors of x is k. In this paper, we study the 1-vertex-magic vertex labelings of two families of disconnected graphs, namely a disjoint union of m copi...

The selective and extensive 13C labeling of mostly hydrophobic amino acid residues in a 25 kDa membrane protein, the colicin Ia channel domain, is reported. The novel 13C labeling approach takes advantage of the amino acid biosynthetic pathways in bacteria and suppresses the synthesis of the amino acid products of the citric acid cycle. The selectivity and extensiveness of labeling significantl...

A graph G = (V, E) is said to be magic if there exists an integer labeling f : V ∪ E −→ [1, |V ∪ E|] such that f(x) + f(y) + f(xy) is constant for all edges xy ∈ E. Enomoto, Masuda and Nakamigawa proved that there are magic graphs of order at most 3n + o(n) which contain a complete graph of order n. Bounds on Sidon sets show that the order of such a graph is at least n + o(n). We close the gap ...