Related papers: On the Irregularity of Some Molecular Structures
Pseudobinary heterostructural alloys of ZnO with MgO or CdO are studied by composing the system locally of clusters with varying ratio of cations. We investigate fourfold (wurtzite structure) and sixfold (rocksalt structure) coordination of…
Praeger-Xu graphs are connected, symmetric, 4-regular graphs that are unusual both in that their automorphism groups are large, and in that vertex stabilizer subgroups are also large. Determining number and distinguishing number are…
This paper deals with the modular irregularity strength of a graph of n vertices, a new graph invariant, modified from the irregularity strength, by changing the condition of the vertex-weight set associate to the well-known irregular…
Highly regular graphs for which not all regularities are explainable by symmetries are fascinating creatures. Some of them like, e.g., the line graph of W.~Kantor's non-classical $\mathrm{GQ}(5^2,5)$, are stumbling stones for existing…
Granularity, anisotropy, local lattice distortions and their dependence on dopant concentration appear to be present in all cuprate superconductors, interwoven with the microscopic mechanisms responsible for superconductivity. Here we…
The gauge invariant elastic metric on the shape space of surfaces involves the mean curvature and the normal deformation, i.e. the sum and the difference of the principal curvatures $\kappa_1,\kappa_2$. The proposed gauge invariant elastic…
The Graovac-Pisanski index, which is also called the modified Wiener index, considers the symmetries and the distances in molecular graphs. Carbon nanotubes are molecules made of carbon with a cylindrical structure possessing unusual…
Topological indices are numerical invariants derived from molecular graphs and play an important role in characterizing chemical compounds and predicting their properties. Among the earliest descriptors are the classical Zagreb indices…
Analysis of chemical graphs is a major research topic in computational molecular biology due to its potential applications to drug design. One approach is inverse quantitative structure activity/property relationship (inverse QSAR/QSPR)…
We compare the various chirality measures most widely used in the literature to quantify chiral symmetry in extended solids, i.e., the continuous chirality measure, the Hausdorff distance, and the angular momentum. By studying these…
The knowledge of transitions between regular, laminar or chaotic behavior is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there…
We use molecular dynamics to study the ordering of a nematic liquid crystal around a spherical particle or droplet. Homeotropic boundary conditions and strong anchoring create a hedgehog director configuration on the particle surface and in…
Enumerating chemical graphs satisfying given constraints is a fundamental problem in mathematical and computational chemistry, and plays an essential part in a recently proposed framework for the inverse QSAR/QSPR. In this paper,…
We study characteristics which might distinguish two-graphs by introducing different numerical measures on the collection of graphs on $n$ vertices. Two conjectures are stated, one using these numerical measures and the other using the deck…
We study pseudo-geometric strongly regular graphs whose second subconstituent with respect to a vertex is a cover of a strongly regular graph or a complete graph. By studying the structure of such graphs, we characterize all graphs…
Configurations are necklaces with prescribed numbers of red and black beads. Among all possible configurations, the regular one plays an important role in many applications. In this paper, several aspects of regular configurations are…
This paper establishes sharp bounds for the vulnerability measures of closeness and generalized closeness in graphs and identifies graphs that attain these bounds. It further develops bounds incorporating Zagreb indices for triangle- and…
The main difficulty of statistical theories of fluid turbulence is the lack of an obvious small parameter. In this paper we show that the formerly established fusion rules can be employed to develop a theory in which Kolmogorov's statistics…
Computer or communication networks are so designed that they do not easily get disrupted under external attack and, moreover, these are easily reconstructible if they do get disrupted. These desirable properties of networks can be measured…
We study theoretically the shapes of biological tubes affected by various pathologies. When epithelial cells grow at an uncontrolled rate, the negative tension produced by their division provokes a buckling instability. Several shapes are…