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...

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...

In this study, using methacrylic and ascorbic acid in gelatin initiated by copper (MAGIC-f) polymer gel after megavoltage energy exposure, the sensitivity of the ultrasound velocity and attenuation coefficient dose-dependent parameters was evaluated. The MAGIC-f polymer gel was irradiated under 1.25 MeV cobalt-60, ranging from 0 to 60 Gy in 2-Gy steps, and received dose uniformity and accuracy ...

ARTICLE INFO An H-magic labeling in a H-decomposable graph G is a bijection f : V (G) ∪ E(G) → {1, 2, ..., p+ q} such that for every copy H in the decomposition, ∑

We present an experimental study of the lattice-induced light shifts on the (1)S(0) --> (3)P(0) optical clock transition (nu(clock) approximately 518 THz) in neutral ytterbium. The "magic" frequency nu(magic) for the 174Yb isotope was determined to be 394 799 475(35) MHz, which leads to a first order light shift uncertainty of 0.38 Hz. We also investigated the hyperpolarizability shifts due to ...

A new family of composite decoupling sequences designed for heteronuclear broadband decoupling of spin-l and spin-f in solids and liquid crystals is introduced. The pulse sequences are windowless and perform net rotations in spin space about magic-angle axes. Computer simulations and experimental results are presented to demonstrate their decoupling performance and to discuss their susceptibili...