A graph is called magic (supermagic) if it admits a labelling of the edges by pairwise different (and consecutive) positive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In the paper we prove that any balanced bipartite graph with minimum degree greater than |V (G)|/4 ≥ 2 is magic. A similar result is presented for supermag...

We consider two innnite games, played on a countable graph G given with an integer vertex labelling. One player seeks to construct a ray (a one-way innnite path) in G, so that the ray's labels dominate or elude domination by an integer sequence being constructed by another player. For each game, we give a structural characterization of the graphs on which one player or the other can win, provid...

In this paper, we propose an approach for doing Gene Ontology (GO) annotation on biomedical texts. The GO is an effort to create a controlled terminology for labelling gene functions in a more precise. Our system is based on the application of Parametrized Finite-State Graphs (P-FSG) for GO tagging. This process was implemented to the annotation of genes related with Alzehimer disease. This pro...

Deuterium labelling is used to show that the disproportionation of thioxanthylium salts involve transfer of a hydride, (deuteride) ion from the9-positionof one molecule of the compound, as its hydro], to the 9 - position of another molecule in the cation form

An orthogonal double cover (ODC) of a graph H is a collection ( ) { } v G v V H : = ∈  of ( ) V H subgraphs (pages) of H, so that they cover every edge of H twice and the intersection of any two of them contains exactly one edge. An ODC  of H is cyclic (CODC) if the cyclic group of order ( ) V H is a subgroup of the automorphism group of  . In this paper, we introduce a general orthogonal la...

The bandwidth b(G) of a graph G is defined by b(G) = min max 1A(-)-X(y)1 A e={x,y} where e ranges over all edges of G and A ranges over all 1 1 functions A :V(G) -> Z , the positive integers . In this note we show for any graph G on n vertices (with G denoting its complement), b(G) + b(G) > n 2 Furthermore, for all n > 3 there exist graphs which achieve this bound . We also prove : (i) b(G) + b...

We exhibit a graceful labelling for each generalised Petersen graph P8t,3 with t ≥ 1. As an easy consequence, we obtain that for any fixed t the corresponding graph is the unique starter graph for a cyclic edgedecomposition of the complete graph K2t+1. Due to its extreme versatility, the technique employed looks promising for finding new graceful labellings, not necessarily involving generalise...

We prove an analog of the classical Hartogs extension theorem for CR L2 functions defined on boundaries of certain (possibly unbounded) domains on coverings of strongly pseudoconvex manifolds. Our result is related to a question formulated in the paper of Gromov, Henkin and Shubin [GHS] on holomorphic L2 functions on coverings of pseudoconvex manifolds.

a. To check that the graph is represented correctly, Bob asks Alice to remove all the paper cups covering the endpoints of every edge. This reveals an isomorphism to the original graph, which Bob cannot check efficiently; thus, Bob also removes the paper cups corresponding to the green numbers, revealing the original labelling of the vertices. This reveals nothing about the vertex cover, but al...