{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Ch03 Graph Theory 1s09

# Ch03 Graph Theory 1s09 - Chapter 3 Topology Topology is a...

This preview shows pages 1–3. Sign up to view the full content.

Fundamentals of Graph Fundamentals of Graph Theory Theory Chapter 3 Artemio P. Magabo Artemio P. Magabo Professor of Electrical Engineering Department of Electrical and Electronics Engineering University of the Philippines - Diliman Department of Electrical and Electronics Engineering Topology Topology is a branch of geometry that concerns with the properties of a geometric figure that are not changed when the figure is twisted, bent, folded, stretched or tied in knots, provided that no parts of the figure are cut apart or joined together. A graph is a picture of an electric circuit where each element has been replaced by a line segment. 3 Ω 4V + - 2A + - V x + - 5V x 1 Ω 2 Ω Department of Electrical and Electronics Engineering Definitions Node – a point of connection of two or more elements Path - a set of elements that may be traversed in order without passing through the same node twice Branch - a single path, containing one simple element, which connects one node to another node Loop - a closed path Mesh - a loop which does not contain any other loop within it Department of Electrical and Electronics Engineering Sub-graph – the graph formed after some branches are removed from the original graph Planar Graph - a graph which may be drawn on a plane surface in such a way that no branch passes over or under any other branch Non-planar Graph - a graph which is not planar These planar graphs are topologically equivalent. d b c a c b d a a c d b n=4 b=6

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Department of Electrical and Electronics Engineering n=6 b=9 This graph is non-planar. n=5 b=9 This graph is planar. Department of Electrical and Electronics Engineering Tree - a subgraph with the following properties: 1. It contains all the nodes of the original graph. No node is left in isolation.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern