The Gram dimension gd(G) of a graph G is the smallest integer k ≥ 1 such that any partial real symmetric matrix, whose entries are specified on the diagonal and at the off-diagonal positions corresponding to edges of G, can be completed to a positive semidefinite matrix of rank at most k (assuming a positive semidefinite completion exists). For any fixed k the class of graphs satisfying gd(G) ≤...

A cycle-transversal of a graph G is a subset T ⊆ V (G) such that T ∩V (C) 6= ∅ for every cycle C of G. A clique cycle-transversal, or cct for short, is a cycle-transversal which is a clique. Recognizing graphs which admit a cct can be done in polynomial time; however, no structural characterization of such graphs is known. We characterize distancehereditary graphs admitting a cct in terms of fo...

We collect some general results on graph limits associated to hereditary classes of graphs. As examples, we consider some classes defined by forbidden subgraphs and some classes of intersection graphs, including triangle-free graphs, chordal graphs, cographs, interval graphs, unit interval graphs, threshold graphs, and line graphs.

Clique-width of graphs is a major new concept with respect to efficiency of graph algorithms. The notion of clique-width extends the one of treewidth, since bounded treewidth implies bounded clique-width. We give a complete classification of all graph classes defined by forbidden induced subgraphs of at most four vertices with respect to bounded or unbounded clique-width.

We continue a recent systematic study into the clique-width of (H1, H2)-free graphs and present five new classes of (H1, H2)-free graphs of bounded clique-width. As a consequence, we have reduced the number of open cases from 13 to 8. Four of the five new graph classes have in common that one of their two forbidden induced subgraphs is the triangle. As such, we generalize corresponding results ...

Let G and H be graphs. A substitution of H in G instead of a vertex v 2 V (G) is the graph G(v ! H), which consists of disjoint union of H and G ? v with the additional edge-set fxy : x 2 V (H); y 2 N G (v)g. For a hereditary class of graphs P, the substitutional closure of P is deened as the class P consisting of all graphs which can be obtained from graphs in P by repeated substitutions. Let ...

It is argued that the prevailing definition of quasicrystals, requiring them to contain an axis of symmetry that is forbidden in periodic crystals, is inadequate. This definition is too restrictive in that it excludes an important and interesting collection of structures that exhibit all the well-known properties of quasicrystals without possessing any forbidden symmetries.

Representative strains of Serratia marcescens from an edible cactus plant and silkworms were characterized and a comparison based on their cellular fatty acid composition, 16S rRNA and groE gene sequence analysis as well as silkworm virulence and chitosan susceptibility was carried out. Results from this study indicate that there are no significant differences between the phenotypic and molecul...

b1-xlaxfeo3 (x = 0.0, 0.025) crystallites were prepared by chemical solution route. xrd analysis confirmed the phase formation of the materials. thermal characterization was done by dsc-tga to confirm crystallization and thermal behavior for phase development. morphological studies by fesem showed the agglomerated nature of the ferrite and edx analysis confirmed the degree of doping. ftir studi...

Domain decomposition is one of the most eeective and popular parallel computing techniques for solving large scale numerical systems. In the special case when the amount of computation in a subdomain is proportional to the volume of the subdomain, domain decomposition amounts to minimizing the surface area of each subdomain while dividing the volume evenly. Motivated by this fact, we study the ...