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grafi nel mondo reale:

grafi nel mondo reale:. reti stradali. nodi = incroci, archi = strade. internet. nodi = pagine, archi = links. incontri sportivi. nodi = squadre, archi = incontri. reti elettriche. nodi = connessioni, archi = elementi. nodi = persone , archi = amicizie. facebook.

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grafi nel mondo reale:

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  1. grafi nel mondo reale: reti stradali nodi = incroci, archi = strade internet nodi = pagine, archi = links incontri sportivi nodi = squadre, archi = incontri reti elettriche nodi = connessioni, archi = elementi nodi = persone, archi = amicizie facebook nodi = posizioni, archi = mosse giochi

  2. ognuno amico di tutti gli altri GRAFO COMPLETO

  3. nessuno amico di nessuno

  4. sottografo completo -> cricca (clique)

  5. un’ altra cricca

  6. c’è almeno una persona con un numero pari di amici ?

  7. grado di un nodo = numero nodi adiacenti somma dei gradi per ogni nodo = 2 volte numero degli archi numero nodi con grado dispari è pari come dimostrare per induzione ?

  8. A: ho 4 amici in (A,B,C,D,E) B: ho 3 amici in (A,B,C,D,E) C: ho 3 amici in (A,B,C,D,E) D: ho 2 amici in (A,B,C,D,E) E: ho 2 amici in (A,B,C,D,E) 5 persone dicono è possibile ?

  9. A B C E D A B C D E 4 3 3 2 2

  10. A B C E D B C D E 2 2 1 1

  11. A B C E D B C D E 2 2 1 1

  12. A B C E D C D E 1 0 1

  13. A B C E D A B C E D C D E 1 0 1 la soluzione è unica ?

  14. A B C E D A B C E D sono diversi, ma se non si tiene conto dei nomi, sono uguali hanno la stessa forma -> isomorfi

  15. non isomorfi

  16. A B C E D A B C D E 4 4 4 2 2

  17. A B C E D B C D E 3 3 1 1

  18. A B C E D B C D E 3 3 1 1

  19. A B C E D C D E 2 0 0

  20. 3 brocche: capacità 8, 5, 3 litri come ottenere 4 litri ? nodi=particolare distribuzione dei litri archi=mosse=versamenti ammissibili

  21. siccome la somma totale è costante basta indicare il contenuto delle brocche piccole (0,0); (0,1); (0,2); (0,3); (1,0); (1,1); (1,2); (1,3); (2,0); (2,1); (2,2); (2,3); (3,0); (3,1); (3,2); (3,3); (4,0); (4,1); (4,2); (4,3); (5,0); (5,1); (5,2); (5,3); hmm… servono proprio tutti ?

  22. (0,0); (0,1); (0,2); (0,3); (1,0); (1,1); (1,2); (1,3); (2,0); (2,1); (2,2); (2,3); (3,0); (3,1); (3,2); (3,3); (4,0); (4,1); (4,2); (4,3); (5,0); (5,1); (5,2); (5,3); possibile che nessuna brocca sia piena oppure vuota? NO

  23. (0,0); (0,1); (0,2); (0,3); (1,0); (1,1); (1,2); (1,3); (2,0); (2,1); (2,2); (2,3); (3,0); (3,1); (3,2); (3,3); (4,0); (4,1); (4,2); (4,3); (5,0); (5,1); (5,2); (5,3); da escludere i casi in cui nessuna brocca è piena oppure vuota

  24. (0,1) (0,2) (0,0) (0,3) (1,0) (1,3) (2,0) (2,3) (3,0) (3,3) (4,0) (4,3) (5,0) (5,1) (5,2) (5,3)

  25. (0,1) (0,2) (0,0) (0,3) (1,0) (1,3) (2,0) (2,3) (3,0) (3,3) (4,0) (4,3) (5,0) (5,1) (5,2) (5,3)

  26. (0,1) (0,2) (0,0) (0,3) (1,0) (1,3) (2,0) (2,3) (3,0) (3,3) (4,0) (4,3) (5,0) (5,1) (5,2) (5,3)

  27. (0,1) (0,2) (0,0) (0,3) (1,0) (1,3) (2,0) (2,3) (3,0) (3,3) (4,0) (4,3) (5,0) (5,1) (5,2) (5,3)

  28. (0,1) (0,2) (0,0) (0,3) (1,0) (1,3) (2,0) (2,3) (3,0) (3,3) (4,0) (4,3) (5,0) (5,1) (5,2) (5,3)

  29. (0,1) (0,2) (0,0) (0,3) (1,0) (1,3) (2,0) (2,3) (3,0) (3,3) (4,0) (4,3) (5,0) (5,1) (5,2) (5,3)

  30. (0,1) (0,2) (0,0) (0,3) (1,0) (1,3) (2,0) (2,3) (3,0) (3,3) (4,0) (4,3) (5,0) (5,1) (5,2) (5,3)

  31. (0,1) (0,2) (0,0) (0,3) (1,0) (1,3) (2,0) (2,3) (3,0) (3,3) (4,0) (4,3) (5,0) (5,1) (5,2) (5,3)

  32. (0,1) (0,2) (0,0) (0,3) (1,0) (1,3) (2,0) (2,3) (3,0) (3,3) (4,0) (4,3) (5,0) (5,1) (5,2) (5,3)

  33. (0,1) (0,2) (0,0) (0,3) (1,0) (1,3) (2,0) (2,3) (3,0) (3,3) (4,0) (4,3) (5,0) (5,1) (5,2) (5,3)

  34. (0,1) (0,2) (0,0) (0,3) (1,0) (1,3) (2,0) (2,3) (3,0) (3,3) (4,0) (4,3) (5,0) (5,1) (5,2) (5,3)

  35. (0,1) (0,2) (0,0) (0,3) (1,0) (1,3) (2,0) (2,3) (3,0) (3,3) (4,0) (4,3) (5,0) (5,1) (5,2) (5,3)

  36. (0,1) (0,2) (0,0) (0,3) (1,0) (1,3) (2,0) (2,3) (3,0) (3,3) (4,0) (4,3) (5,0) (5,1) (5,2) (5,3)

  37. (0,1) (0,2) (0,0) (0,3) (1,0) (1,3) (2,0) (2,3) (3,0) (3,3) (4,0) (4,3) (5,0) (5,1) (5,2) (5,3)

  38. (8,0,0) (7,1,0) (7,0,1) (6,2,0) (6,0,2) (5,0,3) (5,3,0) (4,4,0) (4,0,4) (3,5,0) (3,0,5) (2,6,0) (2,0,6) (1,0,7) (1,7,0) (0,0,8) (0,8,0)

  39. (8,0,0) (7,1,0) (7,0,1) (6,2,0) (6,0,2) (5,0,3) (5,3,0) (4,4,0) (4,1,3) (3,5,0) (3,2,3) (2,5,1) (2,3,3) (1,5,2) (1,4,3) (0,5,3)

  40. (8,0,0) (7,1,0) (7,0,1) (6,2,0) (6,0,2) (5,0,3) (5,3,0) (4,4,0) (4,1,3) (3,5,0) (3,2,3) (2,5,1) (2,3,3) (1,5,2) (1,4,3) (0,5,3)

  41. (8,0,0) (7,1,0) (7,0,1) (6,2,0) (6,0,2) (5,0,3) (5,3,0) (4,4,0) (4,1,3) (3,5,0) (3,2,3) (2,5,1) (2,3,3) (1,5,2) (1,4,3) (0,5,3)

  42. (8,0,0) (7,1,0) (7,0,1) (6,2,0) (6,0,2) (5,0,3) (5,3,0) (4,4,0) (4,1,3) (3,5,0) (3,2,3) (2,5,1) (2,3,3) (1,5,2) (1,4,3) (0,5,3)

  43. (8,0,0) (7,1,0) (7,0,1) (6,2,0) (6,0,2) (5,0,3) (5,3,0) (4,4,0) (4,1,3) (3,5,0) (3,2,3) (2,5,1) (2,3,3) (1,5,2) (1,4,3) (0,5,3)

  44. (8,0,0) (7,1,0) (7,0,1) (6,2,0) (6,0,2) (5,0,3) (5,3,0) (4,4,0) (4,1,3) (3,5,0) (3,2,3) (2,5,1) (2,3,3) (1,5,2) (1,4,3) (0,5,3)

  45. (8,0,0) (7,1,0) (7,0,1) (6,2,0) (6,0,2) (5,0,3) (5,3,0) (4,4,0) (4,1,3) (3,5,0) (3,2,3) (2,5,1) (2,3,3) (1,5,2) (1,4,3) (0,5,3)

  46. (8,0,0) (7,1,0) (7,0,1) (6,2,0) 7 versamenti (6,0,2) (5,0,3) (5,3,0) (4,4,0) (4,1,3) (3,5,0) (3,2,3) (2,5,1) (2,3,3) (1,5,2) (1,4,3) (0,5,3)

  47. (8,0,0) (7,1,0) (7,0,1) (6,2,0) 6 versamenti (6,0,2) (5,0,3) (5,3,0) (4,4,0) (4,1,3) (3,5,0) (3,2,3) (2,5,1) (2,3,3) (1,5,2) (1,4,3) (0,5,3)

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