1 / 3

Euler’s Path Theorem

Euler’s Path Theorem. If a graph is connected and has exactly two odd vertices then it is a Euler path. Any such path starts with an odd vertices and ends at the other one. If a graph has more than two odd vertices it CANNOT be a Euler path. Open Unicursal (start and end is different)

nadine-burgess
Download Presentation

Euler’s Path Theorem

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Euler’s Path Theorem If a graph is connected and has exactly two odd vertices then it is a Euler path. Any such path starts with an odd vertices and ends at the other one. If a graph has more than two odd vertices it CANNOT be a Euler path. Open Unicursal (start and end is different) **Euler proved that you cannot have a graph with just 1 odd vertex.**

  2. Euler’s Circuit Theorem • If a graph is connected and every vertex is even then it has an Euler’s circuit (at least one). • If a graph has any odd vertices then it does not have an Euler’s Circuit • Closed Unicursal • Even means you have as many edges coming in as you have leaving the vertex

More Related