1 / 8

Graph Theory: Chains (Paths) and Cycles (Circuits)

Graph Theory: Chains (Paths) and Cycles (Circuits). Even more terminology. Chain (Path): Sequence of edges where you do not start and end at the same vertex Simple chain : Does not repeat an edge Length : number of edges in the chain

tamar
Télécharger la présentation

Graph Theory: Chains (Paths) and Cycles (Circuits)

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. Graph Theory: Chains (Paths) and Cycles (Circuits)

  2. Even more terminology • Chain (Path): Sequence of edges where you do not start and end at the same vertex • Simple chain: Does not repeat an edge • Length: number of edges in the chain • Distance: written as d(A, B) and is equal to the shortest length connecting two vertices • Cycle (Circuit): A chain beginning and ending at the same vertex • Simple cycle: does not pass through the same edge more than once.

  3. Ex C. B. D. .E A.

  4. Chain: ABCDE, ABCDC, ABCE • Simple chain: ABCDE, ABCE • Length: ABCDE = 4, ABCDC = 4, ABCE = 3 • Distance (A, E) = 2 • Cycle: ABCDA, ABCDECDA,DCED • Simple cycle: ABCDA, DCED

  5. Euler Chain and Cycle Euler Chain: A chain that passes through each vertex once and only once (do not end where you start) Euler Cycle: A cycle that passes through each vertex once and only once (must end where you start)

  6. Ex Euler Chain: BACDBC A. B. .C .D

  7. Ex Euler Cycle: ACDBA A. B. .C .D

  8. How to tell if there is a Euler Chain or Cycle • If each vertex has an even degree = Euler cycle • If there are exactly 2 vertices with odd degree = Euler chain

More Related