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...

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...

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...

Automatic image segmentation and semantic labeling is one of the most important and challenging problems in computer vision. Labeling could be done at various quantization levels – pixel level, super-pixel level, or group of superpixel (segment) level. Each approach has its advantages and disadvantages. In this paper, we explore the superpixel level semantic labeling of images using supervised ...