Ruma Kareem K. Ajeena
The Graphs and their Applications in the Real Life
Recently, graph theory has established itself as an important mathematical tool to solve many real life problems in Mathematical Research, Electrical Engineering, Computer Programming, Computer Networking, Business Administration, Sociology, Economics, Marketing, and Telecommunication. The graph theory has emerged as a mathematical discipline in its own right as well. The real life problems can be modeled with paths formed along the edges of a certain graph.
In this lecture, a brief introduction about the graphs theory has been discussed. This introduction includes the fundamental concepts about the graphs, types of the graphs, how to represent a graph as a matrix in two kinds. Path and cycle graphs and trees. Also, the sub-graphs and how to represent them as a vector space.
This lecture focuses on the applications of the graphs in the real life. One of them is the Network Flows which is considered by a network of pipelines of oil, gas, water, and so on. This network has the values that allows to flow only in one direction with a capacity which is determined on each pipe. A network flows can be represented by a weighted connected graph. The stations are represented by vertices, lines of item such as oil, gas, water or other flows represented by edges and the capacities by weights. An important thing is to determine the maximal flow from source vertex to sink vertex in all these types of this network.
Another perspective has been discussed, it is to use some directed connected graph and its incidence matrix to represent the GPS networks. The information of the GPS graph is maintained by an incidence matrix that can be used to read the set of independent loops in the GPS network.
The problems of efficiently planning routes for flight networks, railway trains, mail delivery, garbage pickup, snow removal, diagnostics in computer networks can be solved using model that involve paths in graph. Also, traveling salesperson problem (TSP), cable laying to connect towns, network analysis in Geographic Information System (GIS), minimum-spanning trees, and so forth. Also, the graph theory plays a vital role in coding theory, communication networks and their security etc. The concepts of graph theory that can be used in different areas of Cryptography. It is widely used as a tool of encryption schemes to speed up the computations, because of its various properties and easy representation as the vectors and matrices.
As well as, several applications of the graph coloring have been determined in different area. These applications are:
- Examination schedules at universities or any educational institutions.
- The relationship between the people.
- Maps coloring and Roadmaps models.
- Visualizing the ecosystem of wildlife.
- Creating a computer network with multiple links.
- Operating the frequency assignments of television channels.
Finally, it is possible to think well about using the graph theory to solve other real life problems through the connection between the concepts of the graphs and the field that the problem related to it.
Graphs, Sub-graphs, Paths, Trees, Minimum-spanning trees, Graph coloring, Real life problems.
Ruma Kareem K. Ajeena was born in Baghdad, Iraq in 1976. She has completed her PhD in Elliptic Curve Cryptography at Mathematical Sciences School, Universiti Sains Malaysia (USM), Penang, Malaysia in 2015. Her research interests are in the areas of Pure and Applied Mathematics, Graph theory, Numerical Algorithms, Information Technology, Coding Theory, Complexity, Cryptography, Security. She has presented her research findings in many international conferences and published many research articles up to more than 50 papers in Clarivate Analytics and Scopus international journals. She is a member of editorial board and reviewer at several journals of pure and applied mathematics and informatics. Also, she has been selected to be a Plenary Speaker, a chair, IEEE Organizing Committee member, a scientific committee member, Judge of sessions at several international IEEE and other conferences. Recently, she has got two awards which are Medals of Creativity at the second international conference of Creativity 2019, Faculty of Nursing, University of Babylon.