Graduate Journal of Interdisciplinary Research, Reports and Reviews

On Vertex-Based Dimension of Some Graphs Joining Certain Prism Graphs

2024-03-17T15:52:41+0530

Background: In graph theory, the prism graph is a type of graph that is characterised by having the structure of a prism as its underlying framework. The notion of a resolving set and that of metric dimension for a graph of a prism is important in uniquely identifying the vertices within a prism graph. For a non-trivial connected graph $\Gamma_{r}=\Gamma_{r}(V, E)$, an ordered subset $U$ of vertices $resolves$ any pair of different vertices $y_{1}, y_{2} \in V$, if $d(v, y_{1})\neq d(v, y_{2})$ for some $v\in U$. Such a set $U$ is said to be a resolving set for $\Gamma_{r}$ and the smallest cardinality of $U$ is called the $metric$ $dimension$ of $\Gamma_{r}$.
Purpose: The purpose of this article is to determine the notion of resolving sets and their corresponding metric dimensions for two complex families of planar graphs obtained by joining $m-$copies of the prism graph on known families of convex polytope graphs.
Methods: The methods used are purely theoretical, based on mathematical reasoning and established definitions related to graph theory.
Results: In this article, we have determined successfully the resolving set and metric dimension for two specific complex families of planar graphs, denoted by $\mathrm{L}_{n}$ and $\mathrm{M}_{n}$, constructed using $m-$copies of a prism graph. These findings contribute to our understanding of these concepts within graph theory.
Conclusions: This research indicates the importance of studying resolving sets and metric dimensions in various graph structures, particularly those derived from multiple copies of the prism graph connected through known families of convex polytope graphs. This work may inspire further investigations into similar graph families or other applications of these concepts in different areas of mathematics and computer science.

Keywords: Metric dimension, independent set, basis set, convex polytope, prism graphs
2000 Mathematics Subject Classification: 05C12

Evaluation of Radioactivity in Tailings From Niobium Mining

2023-12-30T02:09:43+0530

This study evaluates the radioactivity of niobium tailings, based on barite and magnetite concentrates, collected from the exploration of niobium in Araxa city (MG), Brazil. The research is part of a study aimed at using mineral wastes as raw materials for production of cementitious mortars in construction industry. Initially, the samples were monitored using a GM type detector, Gamma spectrometry analysis using a NaI(Tl) detector registered the presence of ²¹⁴Bi and ²⁰⁸Tl above the background radiation in both, samples. Using a HPGe detector, it was possible to calculate the concentrations of ²²⁶Ra and ²²⁸Ra in the barite and magnetite samples, the results were 0.24 ± 0.004 and 0.80 ± 0.003 Bq/g and 0.17 ± 0.01 and 0.87 ± 0.01 Bq/g respectively. The analyses of the results obtained from NAA techniques showed uranium concentration of 5 ± 1μg/g and 12 ± 2μg/g and thorium concentration of 70 ± 1 and 137 ± 2μg/g for barite and magnetite, respectively. The results show that the niobium tailings collected from the mining in Araxá does not represent a radioactivity risk of exposure dose to the public in accordance to the reference values of National Agency CNEN NN 3.01, 2014. Nevertheless, the presence of ²²⁶Ra should be investigated, as it is a source of radon gas exhalation, which can be a risk factor in using these mineral tailing as construction materials.

Effect of Various Reducing Agents On ZnO Nanoparticles Synthesis

2023-09-28T01:49:37+0530

In this study ZnO nanoparticles are prepared by using sol gel method. This method is used by many researchers because of its case of use, easily availability of apparatus, low cost and it is easy to perform. The aim of this research is to study the size of ZnO nanoparticles using different reducing agents like NaOH or NH₃OH or Triton X-100. The used chemicals are highly pure with AR grade. The precipitates were formed and annealed at temperature approx.1000⁰C.The precipitate was collected and characterized by XRD analysis to calculate the crystalline size of the nanoparticles. Nanosized ZnO powder was successfully synthesized and XRD analysis reveal that crystalline size is independent of different reducing agents at 1000⁰C. Also the results obtained show that sol-gel method can produce good quality ZnO particles by using any reducing agents.