scholarly journals The STEM Methodology and Graph Theory: Some Practical Examples

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3110
Author(s):  
Cristina Jordán ◽  
Marina Murillo-Arcila ◽  
Juan R. Torregrosa
Keyword(s):  
Graph Theory ◽  
Undergraduate Students ◽  
Shortest Path ◽  
Real World ◽  
Shortest Path Algorithms ◽  
Real World Problems

In this paper, we highlight that Graph Theory is certainly well suited to an applications approach. One of the basic problems that this theory solves is finding the shortest path between two points. For this purpose, we propose two real-world problems aimed at STEM undergraduate students to be solved by using shortest path algorithms from Graph Theory after previous modeling.

scholarly journals Shortest Path with Dynamic Weight Implementation using Dijkstra’s Algorithm

2016 ◽  
Vol 7 (3) ◽  
pp. 161 ◽  
Author(s):  
Elizabeth Nurmiyati Tamatjita ◽  
Aditya Wikan Mahastama
Keyword(s):  
Shortest Path ◽  
Real World ◽  
Minimum Cost ◽  
Dijkstra’S Algorithm ◽  
Traffic Condition ◽  
The Real ◽  
Dijkstra's Algorithm ◽  
Dynamic Weight ◽  
Shortest Path Algorithms

Shortest path algorithms have been long applied to solve daily problems by selecting the most feasible route with minimum cost or time. However, some of the problems are not simple. This study applied the case using Dijkstra's algorithm on a graph representing street routes with two possible digraphs: one-way and twoway. Each cost was able to be changed anytime, representing the change in traffic condition. Results show that the usage of one way digraph in mapping the route does make the goal possible to reach, while the usage of twoway digraph may cause confusion although it is probably the possible choice in the real world. Both experiments showed that there are no additional computation stresses in re-calculating the shortest path while going halfway to reach the goal.

scholarly journals Certain Properties of Domination in Product Vague Graphs With an Application in Medicine

2021 ◽  
Vol 9 ◽  
Author(s):  
Xiaolong Shi ◽  
Saeed Kosari
Keyword(s):  
Graph Theory ◽  
Real World ◽  
Dominating Set ◽  
Independent Set ◽  
Fuzzy Graph ◽  
Medical Sciences ◽  
Total Dominating Set ◽  
Fuzzy Graphs ◽  
Vague Graph ◽  
Real World Problems

The product vague graph (PVG) is one of the most significant issues in fuzzy graph theory, which has many applications in the medical sciences today. The PVG can manage the uncertainty, connected to the unpredictable and unspecified data of all real-world problems, in which fuzzy graphs (FGs) will not conceivably ensue into generating adequate results. The limitations of previous definitions in FGs have led us to present new definitions in PVGs. Domination is one of the highly remarkable areas in fuzzy graph theory that have many applications in medical and computer sciences. Therefore, in this study, we introduce distinctive concepts and properties related to domination in product vague graphs such as the edge dominating set, total dominating set, perfect dominating set, global dominating set, and edge independent set, with some examples. Finally, we propose an implementation of the concept of a dominating set in medicine that is related to the COVID-19 pandemic.

Chinese Postman Problem

2013 ◽  
pp. 224-228
Author(s):  
Davood Mohammaditabar
Keyword(s):  
Graph Theory ◽  
Real World ◽  
Chinese Postman Problem ◽  
Early Form ◽  
Real World Applications ◽  
Chinese Postman ◽  
Eulerian Tours ◽  
Real World Problems

One of the very popular applications of the graph theory in real world problems is related to the concept of Eulerian tours and trails introduced in Eulerian trail and tours chapter. There are many problems in which users should serve all the connections (edges in a graph, streets of a city, pipelines of a network and etc.) between nodes. In chapter 7 of this book, the existence of such trails and tours in graphs were discussed, and appropriate algorithms were introduced to find Eulerian trails and tour. But in the case a graph does not have such a tour or trail, it’s important to traverse some edges more than once, and this is what usually happens in real world applications. M.K. Kwan in 1962 was the first who introduced this problem as the Chinese postman problem (CPP). The question was that, given a postal zone with a number of streets that must be served by a postal carrier, how can one develop a tour that covers every street in the zone and brings the postman back to his or her point of origin, having traveled the minimum possible distance (Wang et al., 2008)? In this chapter, the Chinese postman problem is discussed, and different variations of it are introduced. Then the very early form of the CPP in which the graph is undirected is explained in more detail.

scholarly journals INTERRUPTED CASE STUDIES IN MATERIALS ENGINEERING

2019 ◽  
Author(s):  
Marta Cerruti
Keyword(s):  
Learning Disabilities ◽  
Case Studies ◽  
Undergraduate Students ◽  
Real World ◽  
Students With Learning Disabilities ◽  
Materials Engineering ◽  
Class Time ◽  
Key Concepts ◽  
Second Year ◽  
Real World Problems

The interrupted case studies method uses case studies taken from real-world problems, and breaks them down in smaller pieces; the students work on the smaller parts in teams during the lecture, and get feedback from the professor before moving on to the next part of the case. I used this approach in a Materials Engineering class taken by undergraduate students in their second year, titled "Analytical and Characterization Techniques". The method engaged the students very effectively during class time and seemed to promote deeper learning of key concepts. The method seemed to be particularly effective with students with learning disabilities.

scholarly journals Handrails through the Swamp? A Pilot to Test the Integration and Implementation Science Framework in Complex Real-World Research

2021 ◽  
Vol 13 (10) ◽  
pp. 5491
Author(s):  
Melissa Robson-Williams ◽  
Bruce Small ◽  
Roger Robson-Williams ◽  
Nick Kirk
Keyword(s):  
Pilot Study ◽  
Case Studies ◽  
Implementation Science ◽  
Real World ◽  
Environmental Problems ◽  
Environmental Research ◽  
Integrative Framework ◽  
The World ◽  
Science Framework ◽  
Real World Problems

The socio-environmental challenges the world faces are ‘swamps’: situations that are messy, complex, and uncertain. The aim of this paper is to help disciplinary scientists navigate these swamps. To achieve this, the paper evaluates an integrative framework designed for researching complex real-world problems, the Integration and Implementation Science (i2S) framework. As a pilot study, we examine seven inter and transdisciplinary agri-environmental case studies against the concepts presented in the i2S framework, and we hypothesise that considering concepts in the i2S framework during the planning and delivery of agri-environmental research will increase the usefulness of the research for next users. We found that for the types of complex, real-world research done in the case studies, increasing attention to the i2S dimensions correlated with increased usefulness for the end users. We conclude that using the i2S framework could provide handrails for researchers, to help them navigate the swamps when engaging with the complexity of socio-environmental problems.

scholarly journals Combined Games with Randomly Delayed Beginnings

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 534
Author(s):  
F. Thomas Bruss
Keyword(s):  
Discrete Time ◽  
Real World ◽  
Optimal Stopping ◽  
Random Variables ◽  
Approximate Solutions ◽  
Real World Problems

This paper presents two-person games involving optimal stopping. As far as we are aware, the type of problems we study are new. We confine our interest to such games in discrete time. Two players are to chose, with randomised choice-priority, between two games G1 and G2. Each game consists of two parts with well-defined targets. Each part consists of a sequence of random variables which determines when the decisive part of the game will begin. In each game, the horizon is bounded, and if the two parts are not finished within the horizon, the game is lost by definition. Otherwise the decisive part begins, on which each player is entitled to apply their or her strategy to reach the second target. If only one player achieves the two targets, this player is the winner. If both win or both lose, the outcome is seen as “deuce”. We motivate the interest of such problems in the context of real-world problems. A few representative problems are solved in detail. The main objective of this article is to serve as a preliminary manual to guide through possible approaches and to discuss under which circumstances we can obtain solutions, or approximate solutions.

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