Course on Graph Theory Essentials Trees and Rook Polynomials
You are interested in Graph Theory and Discrete Mathematics. Graph Theory has tremendous applications in Data Science and Computer Applications. I am Suman Mathews, math educator and teacher.
I have a double master's in Mathematics and have taught Math to college students and High school students. This course will introduce you to trees, a very important part of Graph Theory.
The course starts with the definition of trees, a cycle, a complete graph in relation to a tree. You learn that a connected graph with n vertices and n-1 edges is a tree. The relationship between number of vertices and number of edges in a tree is also shown.
Properties of a tree in Graph Theory such as sum of the degrees of vertices of a tree are discussed with proof. Problems on a tree are also shown.
Rooted trees and it's properties are discussed. What is a root? What is an m-ary tree? You will learn about the relationship between the leaves, internal vertices and number of vertices. Binary trees in Graph Theory is also introduced.
The Merge-Sort Method is taught which teaches you to sort numbers.
You will be introduced to a Forest as a collection of trees. Given 2 trees, and their edge set cardinality, you will learn how to find a relation between their vertex sets. You'll learn about pendant vertices.
If a tree has three vertices of degree two , four vertices of degree three , three vertices of degree four, you will learn how to find the number of pendant vertices in the tree and similar problems.
There is a formula handbook at the end. Learn about Rook polynomials and how to construct basic rook polynomials for 4,5,6,7 squares. Also learn how to apply Rook Polynomials in real life situations.
Learn the basics of Generating Functions.
Enrol for this course and enjoy Trees in Graph Theory. Share this course with your friends who may use this topic.
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