Let F be a graph. A graph G is F -free if it does not contain F as a subgraph. The Turán number of F , written ex(n, F ), is the maximum number of edges in an F -free graph with n vertices. The determination of Turán numbers of bipartite graphs is a challenging and widely investigated problem. In this paper we introduce an ordered version of the Turán problem for bipartite graphs. Let G be a gr...

The polybenzene units BTX 48, X=A (armchair) and X=Z (zig-zag) dimerize forming “eclipsed” isomers, the oligomers of which form structures of five-fold symmetry, called multi-tori. Multi-tori can be designed by appropriate map operations. The genus of multi-tori was calculated from the number of tetrapodal units they consist. A description, in terms of Omega polynomial, of the two linearly peri...

Pre-aggregation of lithium aryloxides into tetrahedral arrangements followed by crystallization with the divergent Lewis base dioxane results in the preparation of three types of coordination polymers: zig-zag chains, (6,3) sheets, and diamondoid lattices.

Communication has to be secure in order to be kept private. The latest developments in the field of digital communication have made secret communication possible. Image hiding is a method in which a secret image is hidden in a cover image thereby forming a hybrid or stego image. In this paper, data hiding is performed by taking difference value of three and two neighbouring pixels by adapting Z...

BACKGROUND Zygomatic implants are an alternative treatment in the rehabilitation of atrophic maxilla to promote stability in the stomatognathic system. The aim of this study was to compare the electromyographic (EMG) activity of masseter and temporalis muscles in controls and in individuals with complete implant-supported dentures anchored in the zygomatic bone. MATERIALS AND METHODS Fifty-fo...

Motile eukaryotic cells migrate with directional persistence by alternating left and right turns, even in the absence of external cues. For example, Dictyostelium discoideum cells crawl by extending distinct pseudopods in an alternating right-left pattern. The mechanisms underlying this zig-zag behavior, however, remain unknown. Here we propose a new Excitable Cortex and Memory (EC&M) model for...

The second Zagreb coindex is a well-known graph invariant defined as the total degree product of all non-adjacent vertex pairs in a graph. The second Zagreb eccentricity coindex is defined analogously to the second Zagreb coindex by replacing the vertex degrees with the vertex eccentricities. In this paper, we present exact expressions or sharp lower bounds for the second Zagreb eccentricity co...