Ondrej Mizera

Lattice and gyroid structures are often subjected to additive technologies to produce various types of products, and the current market has a number of 3D printers that can be used for their production. The quality of the products produced in this way can be assessed on the basis of technical parameters and the filament used. Such an approach, however, is insufficient. In terms of quality, other product parameters need to be assessed, such as the surface texture and the internal structure’s porosity. For such an assessment, we can use the industrial tomography method and the method of roughness measurement via an optical microscope. The paper presents research on the assessment of the surface texture and porosity in lattice and gyroid structures. For the research, two types of test specimens—a specimen with a lattice structure and a specimen with a gyroid structure—were prepared. The obtained results proved that the 3D printing technology directly impacted the surface texture and porosity. For experimental specimens produced by SLS technology, we found that it was very important to carefully remove the excess powder, as unremoved powder can significantly affect the porosity results. For specimens produced by FDM technology, the research confirmed that some “gaps” between the layers were not pores but defects created during specimen production. When analyzing the surface using the Alicon Infinite G5 optical microscope, we found that the measured roughness results were directly impacted by the specimen’s surface color, the structure’s geometry, and the ambient light, which was confirmed by a red lattice experimental specimen, the surface of which could not be scanned. Based on the above, it can be stated that the selection of 3D technology for additive production needs must be given adequate attention regarding the quality of the created structures and textures.

Domination plays an indispensable role in graph theory. Various types of domination explore various types of applications. Equal-status people work together and interlace with each other easily. In this paper, the paired equitable domination of a graph, its inflated graph, and its complement of an inflated graph were studied. The relationship between the domination number of the graph, the equitable domination number, and the paired equitable domination number of complements of the inflated graph were established. Furthermore, we proved the Nordhaus–Gaddum-type inequality, that is, γpre(H)+γpre(H)≤6 if H is a graph with m nodes where m≡0, 2(mod 8) and d(ai) = (m/2) for all ai. The challenges and limitations of this parameter of paired equitable and equitable domination depends on the degree of the vertex of the graph. Practical applications are discussed in various fields and illustrated using the studied parameter.