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Vertex orderings

Vertex orderings. Vertex ordering. 16. 13. 14. 12. 15. 11. 10. 4. 9. 8. 5. 6. 3. 7. 2. 1. t = 16. 13. 14. 12. 15. 11. 10. 4. 9. 8. 5. 6. 3. 7. has two neighbors j , k. 2. s = 1. st -numbering. has two neighbors j , k. st -numbering. t = 16. 13. 14.

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Vertex orderings

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  1. Vertex orderings

  2. Vertex ordering 16 13 14 12 15 11 10 4 9 8 5 6 3 7 2 1

  3. t = 16 13 14 12 15 11 10 4 9 8 5 6 3 7 has two neighbors j, k 2 s = 1 st-numbering

  4. has two neighbors j, k st-numbering t = 16 13 14 12 15 11 10 4 9 8 5 6 3 7 2 s = 1

  5. st-numbering t = 16 13 14 12 15 11 10 4 9 8 5 6 3 7 2 s = 1 and For any i, both vertices induce connected subgraphs.

  6. Application of st-numbersing Planarity testing Visibility drawing Internet routing

  7. Canonical Ordering 16 13 14 15 10 12 11 6 5 9 4 8 7 3 1 2 Triangulated plane graph

  8. Canonical Ordering 16 13 14 15 10 12 11 6 5 9 4 8 7 3 1 2 Gk: subgraph of G induced by vertices

  9. Canonical Ordering 16 13 14 15 10 12 11 6 G9 5 9 4 8 7 3 1 2 Gk: subgraph of G induced by vertices

  10. For any Canonical Ordering 16 13 14 15 10 12 11 6 5 (co1) Gk is biconnected and internally triangulated 9 4 8 7 3 1 2 (co2) vertices 1 and 2 are on the outer face of Gk (co3) vertex k+1 is on the outer face of Gk and the neighbor of k+1 is consecutive on the outer cycle Co(Gk).

  11. For any Canonical Ordering 16 13 14 15 10 12 11 6 5 (co1) Gk is biconnected and internally triangulated 9 4 8 7 3 1 2 G3 (co2) vertices 1 and 2 are on the outer face of Gk (co3) vertex k+1 is on the outer face of Gk and the neighbor of k+1 is consecutive on the outer cycle Co(Gk).

  12. For any Canonical Ordering 16 13 14 15 10 12 11 6 5 (co1) Gk is biconnected and internally triangulated 9 4 8 7 3 1 2 G4 (co2) vertices 1 and 2 are on the outer face of Gk (co3) vertex k+1 is on the outer face of Gk and the neighbor of k+1 is consecutive on the outer cycle Co(Gk).

  13. For any Canonical Ordering 16 13 14 15 10 12 11 6 5 (co1) Gk is biconnected and internally triangulated 9 4 8 7 3 1 2 G10 (co2) vertices 1 and 2 are on the outer face of Gk (co3) vertex k+1 is on the outer face of Gk and the neighbor of k+1 is consecutive on the outer cycle Co(Gk).

  14. For any Canonical Ordering 16 13 14 15 10 12 11 6 5 (co1) Gk is biconnected and internally triangulated 9 4 8 7 3 1 2 G10 (co2) vertices 1 and 2 are on the outer face of Gk (co3) vertex k+1 is on the outer face of Gk and the neighbor of k+1 is consecutive on the outer cycle Co(Gk).

  15. For any Canonical Ordering 16 13 14 15 10 12 11 6 5 (co1) Gk is biconnected and internally triangulated 9 4 8 7 3 1 2 G10 (co2) vertices 1 and 2 are on the outer face of Gk (co3) vertex k+1 is on the outer face of Gk and the neighbor of k+1 is consecutive on the outer cycle Co(Gk).

  16. Straight Line Grid Drawing Straight line grid drawing. Plane graph de Fraysseix et al.’90

  17. Initial drawing of G3

  18. Install k + 1 Gk

  19. Shift and install k + 1 Shift method

  20. Thank You

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