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...

The graphs considered in this paper are finite, undirected and simple. For a graph G, we denote its vertex set by V (G) and its edge set by E(G). A graph labeling, as introduced in [8], is an assignment of integers to the vertices or edges, or both, subject to certain conditions. Over the years, a large variety of different types of graph labelings have been studied, see [2] for an extensive su...

Let G = (V (G), E(G)) be a finite simple graph with p = |V (G)| vertices and q = |E(G)| edges,without isolated vertices or isolated edges. A vertexmagic total labeling is a bijection from V (G) ∪ E(G) to the consecutive integers 1, 2, . . . , p + q, with the property that, for every vertex u in V (G), one has f (u) +  uv∈E(G) f (uv) = k for some constant k. Such a labeling is called E-super ve...

statement of problem: dental plaque is the main source for dental caries and there is no proper vaccine that can affect dental plaques. objectives: daily use of an efficient anti-plaque product can be very beneficial in plaque control and, thus, prevention of caries. this study aims to evaluate the antibacterial effects of four products of chlorhexidine and fluoride on two types of cariogenic b...

Supramolecular hydrogels are composed of self-assembled solid networks that restrict the flow of water. l-Phenylalanine is the smallest molecule reported to date to form gel networks in water, and it is of particular interest due to its crystalline gel state. Single and multi-component hydrogels of l-phenylalanine are used herein as model materials to develop an NMR-based analytical approach to...

Gallian’s survey shows that there is a big variety of labelings of graphs. By means of (di)graphs products we can establish strong relations among some of them. Moreover, due to the freedom of one of the factors, we can also obtain enumerative results that provide lower bounds on the number of nonisomorphic labelings of a particular type. In this talk, we will focus in three of the (di)graphs p...

Abstract We consider Morrey’s open question whether rank-one convexity already implies quasiconvexity in the planar case. For some specific families of energies, there are precise conditions known under which even polyconvexity. will extend these findings to more general family energies $$W{:}{\text {GL}}^+(n)\rightarrow \mathbb {R}$$ <m...