# Discrete structures and graph theory notes pdf

Posted on Thursday, May 20, 2021 3:44:56 AM Posted by Loruhama B. - 20.05.2021

File Name: discrete structures and graph theory notes .zip

Size: 11483Kb

Published: 20.05.2021

It's often said that mathematics is useful in solving a very wide variety of practical problems.

## Graph & Graph Models

The previous part brought forth the different tools for reasoning, proofing and problem solving. In this part, we will study the discrete structures that form the basis of formulating many a real-life problem. The two discrete structures that we will cover are graphs and trees. A graph is a set of points, called nodes or vertices, which are interconnected by a set of lines called edges.

The study of graphs, or graph theory is an important part of a number of disciplines in the fields of mathematics, engineering and computer science.

For the above graph the degree of the graph is 3. If in a graph multiple edges between the same set of vertices are allowed, it is called Multigraph. In other words, it is a graph having at least one loop or multiple edges.

A graph is connected if any two vertices of the graph are connected by a path; while a graph is disconnected if at least two vertices of the graph are not connected by a path. A graph is regular if all the vertices of the graph have the same degree.

A graph is called complete graph if every two vertices pair are joined by exactly one edge. If a graph consists of a single cycle, it is called cycle graph. A complete bipartite graph is a bipartite graph in which each vertex in the first set is joined to every single vertex in the second set. If we draw graph in the plane without edge crossing, it is called embedding the graph in the plane. It is easier to check non-isomorphism than isomorphism.

An Euler path is a path that uses every edge of a graph exactly once. An Euler path starts and ends at different vertices.

An Euler circuit is a circuit that uses every edge of a graph exactly once. An Euler circuit always starts and ends at the same vertex. This is called Dirac's Theorem. This is called Ore's theorem. Previous Page. Next Page. Previous Page Print Page. Dashboard Logout.

## Lecture notes on the Web

A network has points, connected by lines. Rosen , Kamala Krithivasan McGraw-Hill Companies , - Computer science - pages Discrete Mathematics is a branch of mathematics involving discrete elements that uses algebra and arithmetic. In a graph, we have special names for these. Students are strongly encouraged to keep up with the exercises and the sequel of concepts as they are going along, for mathematics builds on itself. However, I wanted to discuss logic and proofs together, and found that doing both This is a course note on discrete mathematics as used in Computer Science. A graph is depicted diagrammatically as a set of dots depicting vertices connected by lines or curves depicting edges. Notes on Discrete Mathematics by James Aspnes.

The previous part brought forth the different tools for reasoning, proofing and problem solving. In this part, we will study the discrete structures that form the basis of formulating many a real-life problem. The two discrete structures that we will cover are graphs and trees. A graph is a set of points, called nodes or vertices, which are interconnected by a set of lines called edges. The study of graphs, or graph theory is an important part of a number of disciplines in the fields of mathematics, engineering and computer science. For the above graph the degree of the graph is 3. If in a graph multiple edges between the same set of vertices are allowed, it is called Multigraph.

In CSX we will assume most of high-school mathematics, including In this course we will introduce the basic concepts and results in graph theory, which.

Copies of the classnotes are on the internet in PDF format as given below. These notes have not been classroom tested and may contain typographical errors. This class no longer exists, but the notes are close to what would be used in our current Mathematical Reasoning MATH class. Syllabus for the class. The Foundations: Logic, Sets, and Functions.

Save extra with 2 Offers. About The Book Discrete Mathematics And Graph Theory Book Summary: This comprehensive and self-contained text provides a thorough understanding of the concepts and applications of discrete mathematics and graph theory. It is written in such a manner that beginners can develop an interest in the subject.

Search this site. A Summary of Progress in Petrography. Aboriginal Australians PDF. Academic Equitation PDF.

### Lecture notes on the Web

Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. Of course, this only really addresses the graph theory from your question above, and much of it is probably at a higher level than you're asking for. Still worth plugging as an excellent resource. Try Discrete mathematics , a set of notes by William Chen. Here are the chapter headings:.

In mathematics , and more specifically in graph theory , a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called vertices also called nodes or points and each of the related pairs of vertices is called an edge also called link or line. Graphs are one of the objects of study in discrete mathematics. The edges may be directed or undirected. For example, if the vertices represent people at a party, and there is an edge between two people if they shake hands, then this graph is undirected because any person A can shake hands with a person B only if B also shakes hands with A.