scholarly journals Student Understanding of Number Line Graphs

2020 ◽  
Author(s):  
Alison Mirin
Keyword(s):  
Line Graph ◽  
College Algebra ◽  
Number Line ◽  
Free Variable ◽  
Student Understanding ◽  
Solution Set ◽  
Future Research ◽  
Line Graphs ◽  
Algebra Students ◽  
Solution Representation

This paper addresses how students understand number line graphs. Utilizing a Think Aloud interview followed by a reflection-eliciting interview, we investigate how two successful College Algebra students understand what it means to graph a statement with one free variable on a number line.  These particular students show a mathematically non-normative understanding of this concept; to wit, they do not view the number line graph as representing a solution set. This study illustrates the importance of future research into how students understand the concept of solution representation via number line graphs.

scholarly journals Topological invariants for the line graphs of some classes of graphs

2019 ◽  
Vol 17 (1) ◽  
pp. 1483-1490
Author(s):  
Xiaoqing Zhou ◽  
Mustafa Habib ◽  
Tariq Javeed Zia ◽  
Asim Naseem ◽  
Anila Hanif ◽  
...  
Keyword(s):  
Communication Theory ◽  
Chemical Reactivity ◽  
Line Graph ◽  
Chemical Properties ◽  
Topological Invariants ◽  
Line Graphs ◽  
Physical And Chemical Properties ◽  
Physical And Chemical ◽  
Ladder Graphs ◽  
And Chemical Properties

AbstractGraph theory plays important roles in the fields of electronic and electrical engineering. For example, it is critical in signal processing, networking, communication theory, and many other important topics. A topological index (TI) is a real number attached to graph networks and correlates the chemical networks with physical and chemical properties, as well as with chemical reactivity. In this paper, our aim is to compute degree-dependent TIs for the line graph of the Wheel and Ladder graphs. To perform these computations, we first computed M-polynomials and then from the M-polynomials we recovered nine degree-dependent TIs for the line graph of the Wheel and Ladder graphs.

scholarly journals A Strengthening of Brooks' Theorem for Line Graphs

10.37236/632 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Landon Rabern
Keyword(s):  
Chromatic Number ◽  
Maximum Degree ◽  
Line Graph ◽  
Clique Number ◽  
Line Graphs ◽  
Delta G

We prove that if $G$ is the line graph of a multigraph, then the chromatic number $\chi(G)$ of $G$ is at most $\max\left\{\omega(G), \frac{7\Delta(G) + 10}{8}\right\}$ where $\omega(G)$ and $\Delta(G)$ are the clique number and the maximum degree of $G$, respectively. Thus Brooks' Theorem holds for line graphs of multigraphs in much stronger form. Using similar methods we then prove that if $G$ is the line graph of a multigraph with $\chi(G) \geq \Delta(G) \geq 9$, then $G$ contains a clique on $\Delta(G)$ vertices. Thus the Borodin-Kostochka Conjecture holds for line graphs of multigraphs.

On Spanning and Dominating Circuits in Graphs

1977 ◽  
Vol 20 (2) ◽  
pp. 215-220 ◽  
Author(s):  
L. Lesniak-Foster ◽  
James E. Williamson
Keyword(s):  
Line Graph ◽  
Dominating Set ◽  
Line Graphs ◽  
Sufficient Condition ◽  
Vertex Set ◽  
On Line ◽  
One To One

AbstractA set E of edges of a graph G is said to be a dominating set of edges if every edge of G either belongs to E or is adjacent to an edge of E. If the subgraph 〈E〉 induced by E is a trail T, then T is called a dominating trail of G. Dominating circuits are defined analogously. A sufficient condition is given for a graph to possess a spanning (and thus dominating) circuit and a sufficient condition is given for a graph to possess a spanning (and thus dominating) trail between each pair of distinct vertices. The line graph L(G) of a graph G is defined to be that graph whose vertex set can be put in one-to-one correspondence with the edge set of G in such a way that two vertices of L(G) are adjacent if and only if the corresponding edges of G are adjacent. The existence of dominating trails and circuits is employed to present results on line graphs and second iterated line graphs, respectively.

scholarly journals A Study on Visual Representations for Active Plant Wall Data Analysis

Data ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 74 ◽  
Author(s):  
Kahin Akram Hassan ◽  
Yu Liu ◽  
Lonni Besançon ◽  
Jimmy Johansson ◽  
Niklas Rönnberg
Keyword(s):  
User Study ◽  
Line Graph ◽  
Well Being ◽  
Future Research ◽  
Temporal Data ◽  
Indoor Climate ◽  
Structured Interviews ◽  
Future Directions ◽  
Domain Experts ◽  
The Status

The indoor climate is closely related to human health, well-being, and comfort. Thus, an understanding of the indoor climate is vital. One way to improve the indoor climates is to place an aesthetically pleasing active plant wall in the environment. By collecting data using sensors placed in and around the plant wall both the indoor climate and the status of the plant wall can be monitored and analyzed. This manuscript presents a user study with domain experts in this field with a focus on the representation of such data. The experts explored this data with a Line graph, a Horizon graph, and a Stacked area graph to better understand the status of the active plant wall and the indoor climate. Qualitative measures were collected with Think-aloud protocol and semi-structured interviews. The study resulted in four categories of analysis tasks: Overview, Detail, Perception, and Complexity. The Line graph was found to be preferred for use in providing an overview, and the Horizon graph for detailed analysis, revealing patterns and showing discernible trends, while the Stacked area graph was generally not preferred. Based on these findings, directions for future research are discussed and formulated. The results and future directions of this research can facilitate the analysis of multivariate temporal data, both for domain users and visualization researchers.

COMPARISON OF STUDENT UNDERSTANDING OF LINE GRAPH SLOPE IN PHYSICS AND MATHEMATICS

2012 ◽  
Vol 10 (6) ◽  
pp. 1393-1414 ◽  
Author(s):  
Maja Planinic ◽  
Zeljka Milin-Sipus ◽  
Helena Katic ◽  
Ana Susac ◽  
Lana Ivanjek
Keyword(s):  
Line Graph ◽  
Student Understanding ◽  
And Mathematics

scholarly journals Efficient Algorithm for Generating Maximal L-Reflexive Trees

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 809
Author(s):  
Milica Anđelić ◽  
Dejan Živković
Keyword(s):  
Efficient Algorithm ◽  
Line Graph ◽  
Common Vertex ◽  
Line Graphs ◽  
Algebraic Numbers ◽  
Pisot Numbers ◽  
Full Characterization ◽  
Vertex Set ◽  
Second Largest Eigenvalue

The line graph of a graph G is another graph of which the vertex set corresponds to the edge set of G, and two vertices of the line graph of G are adjacent if the corresponding edges in G share a common vertex. A graph is reflexive if the second-largest eigenvalue of its adjacency matrix is no greater than 2. Reflexive graphs give combinatorial ground to generate two classes of algebraic numbers, Salem and Pisot numbers. The difficult question of identifying those graphs whose line graphs are reflexive (called L-reflexive graphs) is naturally attacked by first answering this question for trees. Even then, however, an elegant full characterization of reflexive line graphs of trees has proved to be quite formidable. In this paper, we present an efficient algorithm for the exhaustive generation of maximal L-reflexive trees.

Motion Comparison Method Combining Segmented Multi-Joint Line Graphs with the SIFT Matching Technique

2014 ◽  
Vol 599-601 ◽  
pp. 1566-1570
Author(s):  
Ming Zeng ◽  
Hong Lin Ren ◽  
Qing Hao Meng ◽  
Chang Wei Chen ◽  
Shu Gen Ma
Keyword(s):  
Feature Matching ◽  
Line Graph ◽  
Comparison Method ◽  
Joint Line ◽  
Line Graphs ◽  
3D Motion ◽  
Motion Data ◽  
Comparison Results ◽  
Matching Technique ◽  
Sift Features

In this paper, an effective motion comparison method based on segmented multi-joint line graphs combined with the SIFT feature matching method is proposed. Firstly, the multi-joint 3D motion data are captured using the Kinect. Secondly, 3D motion data are normalized and distortion data are removed. Therefore, a 2D line graph can be obtained. Next, SIFT features of the 2D motion line graph are extracted. Finally, the line graphs are divided into several regions and then the comparison results can be calculated based on SIFT matching ratios between the tutor’s local line graph and the trainee’s local line graph. The experimental results show that the proposed method not only can easily deal with the several challenge problems in motion analysis, e.g., the problem of different rhythm of motions, the problem of a large amount of data, but also can provide detailed error correction cues.

scholarly journals Do Graph Readers Prefer the Graph Type Most Suited to a Given Task? Insights from Eye Tracking

2016 ◽  
Vol 9 (4) ◽  
Author(s):  
Benjamin Strobel ◽  
Steffani Saß ◽  
Marlit Annalena Lindner ◽  
Olaf Köller
Keyword(s):  
Eye Tracking ◽  
Task Type ◽  
Mixed Effects Models ◽  
Future Research ◽  
Line Graphs ◽  
Linear Mixed Effects Models ◽  
Linear Mixed Effects ◽  
Graph Comprehension ◽  
Graph Type ◽  
Graph Task

Research on graph comprehension suggests that point differences are easier to read in bar graphs, while trends are easier to read in line graphs. But are graph readers able to detect and use the most suited graph type for a given task? In this study, we applied a dual repre-sentation paradigm and eye tracking methodology to determine graph readers’ preferential processing of bar and line graphs while solving both point difference and trend tasks. Data were analyzed using linear mixed-effects models. Results show that participants shifted their graph preference depending on the task type and refined their preference over the course of the graph task. Implications for future research are discussed.

scholarly journals PRIMARY SCHOOL STUDENTS’ READING LEVELS OF LINE GRAPHS

2021 ◽  
Vol 20 (2) ◽  
pp. 6
Author(s):  
PEDRO ARTEAGA ◽  
DANILO DÍAZ-LEVICOY ◽  
CARMEN BATANERO
Keyword(s):  
Primary School ◽  
Line Graph ◽  
Reading Level ◽  
Primary School Children ◽  
Line Graphs ◽  
School Students ◽  
Reading Levels ◽  
Grade Levels ◽  
Data Value ◽  
Educación Primaria

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.

scholarly journals Line Graphs of Monogenic Semigroup Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-4
Author(s):  
Nihat Akgunes ◽  
Yasar Nacaroglu ◽  
Sedat Pak
Keyword(s):  
Maximum Degree ◽  
Zero Divisor ◽  
Minimum Degree ◽  
Line Graph ◽  
Domination Number ◽  
Clique Number ◽  
Line Graphs ◽  
Monogenic Semigroup ◽  
Graph Properties ◽  
Graph Parameters

The concept of monogenic semigroup graphs Γ S M is firstly introduced by Das et al. (2013) based on zero divisor graphs. In this study, we mainly discuss the some graph properties over the line graph L Γ S M of Γ S M . In detail, we prove the existence of graph parameters, namely, radius, diameter, girth, maximum degree, minimum degree, chromatic number, clique number, and domination number over L Γ S M .

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