1 / 16

The Spanning Trees Formulas in a Class of Double Fixed-Step Loop Networks

The Spanning Trees Formulas in a Class of Double Fixed-Step Loop Networks. Talip Atajan, Naohisa Otsuka Tokyo Denki University, Japan Xuerong Yong University of Puerto Rico, USA. This Talk is Composed of. A double fixed-step loop network An oriented spanning tree Reliability of a network

daleneal
Télécharger la présentation

The Spanning Trees Formulas in a Class of Double Fixed-Step Loop Networks

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. The Spanning Trees Formulas in a Class of Double Fixed-Step LoopNetworks Talip Atajan,Naohisa OtsukaTokyo Denki University, JapanXuerong YongUniversity of Puerto Rico, USA

  2. This Talk is Composed of • A double fixed-step loop network • An orientedspanning tree • Reliability of a network • Designing electrical circuits • Matrix tree theorem • Recurrence formula • A series of formulae for special p, q and n • New techniques

  3. 0 1 15 14 2 3 13 4 12 5 11 10 6 7 9 8 DEFINATION A double fixed-step loop network 4

  4. DEFINATION An orientedspanning tree An orientedspanning tree in a digraph D is a rooted tree with the same vertexset as D, that is, thereis a node specified as the root and fromit there is a path to any vertex of D. 0 1 0 1 0 1 3 2 3 3 2 2 G

  5. APPLICATION • Reliability of a network 0 1 7 2 6 5 3

  6. APPLICATION • Designing electrical circuits • Ohm’s Law • Kirchhoff’s Law

  7. Techniques Matrix Tree Theorem 0 1 3 2 G 0 1 3 2 0 1 3 2

  8. Techniques • Recurrence formula

  9. Techniques • The formulae for

  10. 3,5 C 16 0 3 6 9 0 3 0 6 9 1 15 0 3 6 9 12 13 14 2 12 13 12 13 3 13 15 10 15 10 15 4 10 12 2 7 5 2 2 11 7 7 10 6 5 5 4 4 5 4 7 9 8 1 14 11 8 1 14 11 8 1 14 11 8 Our Results 0 0 15 15 1 1 14 14 2 2 3 3 13 13 4 4 12 12 5 11 11 5 10 10 6 6 9 7 9 8 8 7

  11. Our Results • Theorem 2 (Opposed side of Waring's formula)

  12. Our Results

  13. Our Results • Using Newton's identities

  14. Our Results • Theorem 1

  15. 3,5 C 16 0 1 15 14 2 3 13 4 12 5 11 10 6 7 9 8 Our Results 0 13 14 15 11 12 10 2 3 1 9 7 8 6 5 4 0 15 1 14 2 3 13 4 12 11 5 10 6 9 8 7

  16. Thank you for your attandnce END

More Related