Related papers: On the Irregularity of Some Molecular Structures
Electrical conductivity is the most fundamental charge transport parameter, and measurements of conductivity are a basic part of materials characterization for nearly all conducting materials. In thin films, conductivity is often measured…
Metric anomalies arising from a distribution of point defects (intrinsic interstitials, vacancies, point stacking faults), thermal deformation, biological growth, etc. are well known sources of material inhomogeneity and internal stress. By…
Chemical graph theory is commonly used to analyse and comprehend chemical structures and networks, as well as their features. The resolvability parameters for graph $G$= $(V,E)$ are a relatively new advanced field in which the complete…
Karonski, Luczak, and Thomason (2004) conjectured that, for any connected graph G on at least three vertices, there exists an edge weighting from {1,2,3} such that adjacent vertices receive different sums of incident edge weights.…
A topological index of a graph $G$ is a numerical quantity that describes its topology. Reverse degree-based topological indices play an important role in finding topological descriptors. Azacitidine, Decitabine, and Guadecitabine are…
An edge irregular total $k$-labelling $f : V(G)\cup E(G)\rightarrow \{1,2,\dots,k\}$ of a graph $G$ is a labelling of the vertices and the edges of $G$ in such a way that any two different edges have distinct weights. The weight of an edge…
Topological indices are graph-theoretic descriptors that play a crucial role in mathematical chemistry, capturing the structural characteristics of molecules and enabling the prediction of their physicochemical properties. A widely studied…
This study explores the irregularity properties of trees with prescribed degree sequences by analyzing two prominent topological indices: the Albertson index and the sigma index. With a particular emphasis on caterpillar trees -frequently…
Quantifying the level of atomic disorder within materials is critical to understanding how evolving local structural environments dictate performance and durability. Here, we leverage graph neural networks to define a physically…
We introduce weak oddness $\omega_{\textrm w}$, a new measure of uncolourability of cubic graphs, defined as the least number of odd components in an even factor. For every bridgeless cubic graph $G$, $\rho(G)\le\omega_{\textrm…
Within the standard electroweak model we point out that the $3\times 3$ matrix of quark mixing is characterized by three universal (rephasing-invariant) quantities: one of them for $CP$ violation and the other two for off-diagonal…
A strict lower bound for the diameter of a symmetric graph is proposed, which is calculable with the order $n$ and other local parameters of the graph such as the degree $k\,(\geq 3)$, even girth $g\,(\geq 4)$, and number of $g$-cycles…
We consider the effect of various defects and boundary structures on the low energy electronic properties in conducting zigzag and armchair carbon nanotubes. The tight binding model of the conduction bands is mapped exactly onto simple…
The irregularity strength of a graph $G$, $s(G)$, is the least $k$ such that there exists a $\{1,2,\ldots,k\}$-weighting of the edges of $G$ attributing distinct weighted degrees to all vertices, or equivalently the least $k$ enabling…
Introduced the quantitative measure of the structural complexity of the graph (complex network, etc.) based on a procedure similar to the renormalization process, considering the difference between actual and averaged graph structures on…
Theoretical frameworks used to qualitatively and quantitatively describe nuclear dynamics in solids are often based on the harmonic approximation. However, this approximation is known to become inaccurate or to break down completely in many…
The micro-structure of most of the engineering alloys contains some inclusions and precipitates, which may affect their properties, therefore it is crucial to characterize them. In this work we focus on the development of a state-of-the-art…
Clustering algorithms for large networks typically use modularity values to test which partitions of the vertex set better represent structure in the data. The modularity of a graph is the maximum modularity of a partition. We consider the…
Topological indices are graph invariants numeric quantities, which are utilized by researchers to analyze a variety of physiochemical aspects of molecules. The goal of developing topological indices is to give each chemical structure a…
There are various topological indices for example distance based topological indices and degree based topological indices etc. In QSAR/QSPR study, physiochemical properties and topological indices for example atom bond connectivity index,…