Line graph theory reveals hidden spin frustration and bond frustration in molecular crystals with strong isotropy

Graph theory has demonstrated that only three lattices, namely, honeycomb, K4, and diamond lattices, possess a strong isotropic property. It is also recognized that their line graphs correspond to kagome,...

PRIMARY SCHOOL STUDENTS’ READING LEVELS OF LINE GRAPHS

The aim of this research was to describe the errors and reading levels that 6th and 7th grade Chilean primary school children reach when working with line graphs. To achieve this objective, we gave a questionnaire, previously validated by experts with two open-ended tasks, to a sample of 745 students from different Chilean cities. In the first task, we asked the children to read the title of the graph, describe the variables represented and perform a direct and inverse reading of a data value. In the second task, where we address the visual effect of a scale change in a representation, the students had to select the line graph more convenient to a candidate. Although both tasks were considered easy for the grade levels targeted, only some of the students achieved the highest reading level and many made occasional errors in the reading of the graphs. Abstract: Spanish El objetivo de esta investigación es describir los errores y niveles de lectura que alcanzan estudiantes chilenos de 6º y 7º grado de Educación Primaria al trabajar con gráficos de líneas. Para lograr este objetivo, se aplicó un cuestionario, previamente validado por expertos, con dos tareas abiertas a una muestra de 745 estudiantes de diferentes ciudades chilenas. En la primera tarea, se pidió que leyeran el título del gráfico, indicaran las variables representadas y realizaran una lectura directa y otra inversa de un valor de datos. En la segunda tarea, los estudiantes deben seleccionar y justificar el gráfico de líneas más conveniente para respaldar a un candidato, donde se aborda el efecto visual de cambio de escala en una representación. Aunque ambas tareas fueron fáciles, solo una parte de los estudiantes logró el máximo nivel de lectura y aparecieron errores ocasionales en la lectura de los gráficos.

A Comparative Study of Three Resolving Parameters of Graphs

Graph theory is one of those subjects that is a vital part of the digital world. It is used to monitor the movement of robots on a network, to debug computer networks, to develop algorithms, and to analyze the structural properties of chemical structures, among other things. It is also useful in airplane scheduling and the study of diffusion mechanisms. The parameters computed in this article are very useful in pattern recognition and image processing. A number d f , w = min d w , t , d w , s is referred as distance between f = t s an edge and w a vertex. d w , f 1 ≠ d w , f 2 implies that two edges f 1 , f 2 ∈ E are resolved by node w ∈ V . A set of nodes A is referred to as an edge metric generator if every two links/edges of Γ are resolved by some nodes of A and least cardinality of such sets is termed as edge metric dimension, e dim Γ for a graph Γ . A set B of some nodes of Γ is a mixed metric generator if any two members of V ∪ E are resolved by some members of B . Such a set B with least cardinality is termed as mixed metric dimension, m dim Γ . In this paper, the metric dimension, edge metric dimension, and mixed metric dimension of dragon graph T n , m , line graph of dragon graph L T n , m , paraline graph of dragon graph L S T n , m , and line graph of line graph of dragon graph L L T n , m have been computed. It is shown that these parameters are constant, and a comparative analysis is also given for the said families of graphs.

Non-Hermitian topological states in 2D line-graph lattices: Evolving triple exceptional points on reciprocal line graphs

Non-Hermitian (NH) topological states, such as the doubly-degenerate nodes dubbed as exceptional points (EPs) in Bloch band structure of 2D lattices driven by gain and loss, have attracted much recent interest. We demonstrate theoretically that in the three-site edge-centered lattices, i.e., the so-called line-graph lattices, such as Kagome lattice which is a line graph of hexagonal lattice, there exist three types of triply-degenerate EPs (TEPs) evolving intriguingly on another set of line graphs in the reciprocal space. A single TEP (STEP) with ±1/3 topological charge moves faithfully along the edges of reciprocal line graphs with varying gain and loss, while two STEPs merge distinctively into one unconventional orthogonal double TEP (DTEP) with ±2/3 charge at the vertices, which is characterized with two ordinary self-orthogonal eigenfunctions but one surprising “orthogonal” eigenfunction. Differently, in a modified line-graph lattice with an off-edge-center site, the ordinary coalesced state of DTEPs emerges with three identical self-orthogonal eigenfunctions. Such NH states and their evolution can be generally realized in various artificial systems, such as photonic and sonic crystals, where light and sonic vortex beams with different fractional twisting can be found. Our findings shed new light on fundamental understanding of gapless topological states in NH systems in terms of creation and evolution of high-order EPs, and open up new research directions to further link line graph and flow network theory coupled with topological physics, especially under non-equilibrium gain/loss conditions.

No matter how you mark the points on the fever curve – threatening shapes do not add to threat of climate change

Graphs have become an increasingly important means of representing data, for instance, when communicating data on climate change. However, graph characteristics might significantly affect graph comprehension. The goal of the present work was to test whether the marking forms usually depicted on line-graphs, can have an impact on graph evaluation. As past work suggests that triangular forms might be related to threat, we compared the effect of triangular marking forms with other symbols (triangles, circles, squares, rhombi, and asterisks) on subjective assessments. Participants in Study 1 (N = 314) received 5 different line-graphs about climate change, each of them using one out of 5 marking forms. In Study 1, the threat and arousal ratings of the graphs with triangular marking shapes were not higher than those with the other marking symbols. Participants in Study 2 (N = 279) received the same graphs, yet without labels and indeed rated the graphs with triangle point markers as more threatening. Testing whether local rather than global spatial attention would lead to an impact of marker shape in climate graphs, Study 3 (N = 307) documented that a task demanding to process a specific data-point on the graph (rather than just the line graph as a whole) did not lead to an effect either. These results suggest that marking symbols can principally affect threat and arousal ratings but not in the context of climate change. Hence, in graphs on climate change, choice of point markers does not have to take potential side-effects on threat and arousal into account. These seem to be restricted to the processing of graphs where form aspects face less competition from the content domain on judgments.

Annotation and Classification of Graphs of Property Values Reported in Material Science Literature

Building a system for extracting information from the scientific literature is an important research topic in the field of inorganic materials science. However, conventional extraction systems have a limitation in that they do not extract characteristic values from nontextual components, such as charts, diagrams, and tables, which provide key information in many scientific documents. Although there have been several studies on identifying the characteristic values of graphs in the literature, there is no general method that classifies graphs according to the property conditions of the values in the field of materials science. Therefore, in this study, we focus on graphs that are figures representing graphically numerical data, such as a bar graph and line graph, as the first step toward developing a framework for extracting material property information from such noncontextual components. We propose deep-learning-based classification models for identifying the types of graph properties, such as temperature and time, by combining graph images, text in graphs, and captions in neural networks. To train and evaluate the models, we construct a material graph dataset with different types of material properties from a large collection of data from journals in the field of materials science. By using cloud sourcing, we annotate 16,668 images. Our experimental results demonstrate that the best model can achieve high performance with a microaveraged F-score of 0.961.

On Topological Indices of Total Graph and Its Line Graph for Kragujevac Tree Networks

Kragujevac tree is indicated by K ; K ∈ K g q = s 2 t + 1 + 1 , s with order and size s 2 t + 1 + 1 and s 2 t + 1 , respectively. In this paper, we have a look at certain topological features of the total graph and line graph of the total graph of the considered tree, i.e ., Kragujevac tree, by computing different topological indices and polynomials.

Atomistic Line Graph Neural Network for improved materials property predictions

Graph neural networks (GNN) have been shown to provide substantial performance improvements for atomistic material representation and modeling compared with descriptor-based machine learning models. While most existing GNN models for atomistic predictions are based on atomic distance information, they do not explicitly incorporate bond angles, which are critical for distinguishing many atomic structures. Furthermore, many material properties are known to be sensitive to slight changes in bond angles. We present an Atomistic Line Graph Neural Network (ALIGNN), a GNN architecture that performs message passing on both the interatomic bond graph and its line graph corresponding to bond angles. We demonstrate that angle information can be explicitly and efficiently included, leading to improved performance on multiple atomistic prediction tasks. We ALIGNN models for predicting 52 solid-state and molecular properties available in the JARVIS-DFT, Materials project, and QM9 databases. ALIGNN can outperform some previously reported GNN models on atomistic prediction tasks by up to 85% in accuracy with better or comparable model training speed.

Subgraph of generalized co-maximal graph of commutative rings

Let R be a commutative ring with 1. In [3], we introduced a graph G(R) whose vertices are elements of R and two distinct vertices a, b are adjacent if and only if aR + bR = eR for some non-zero idempotent e in R. Let G′(R) be the subgraph of G(R) generated by the non-units of R. In this paper, we characterize those rings R for which the graph G′(R) is connected and Eulerian. Also we characterize those rings R for which genus of the graph G′(R) is ≤ 2. Finally, we show that the graph G′(R) is a line graph of some graph if and only if R is either a regular ring or a local ring.AMS Subject Classification 2020 : 05C25

On Analysis of Topological Aspects for Subdivision of Kragujevac Tree Networks

In this paper, we have taken review of certain topological topological characteristics of subdivision and the line graph of subdivision of Kragujevac tree. A Kragujevac tree is denoted by K , K ∈ Kg q = r 2 t + 1 + 1 , r , with order r 2 t + 1 + 1 and size r 2 t + 1 , respectively. We have computed the Zagreb polynomials, forgotten polynomial, and M-polynomial for Kragujevac tree. Moreover, we have computed topological indices like Zagreb-type indices, reduced reciprocal Randić indices, family of Gourava indices as well as forgotten index. Further, some topological indices that can be directly derived from M-polynomial, i.e., first and second Zagreb index, modified second Zagreb index, Randić and reciprocal Randić index, symmetric division and harmonic index, and inverse sum and augmented Zagreb index are also computed.