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Reprezentarea grafurilor orientate

Reprezentarea grafurilor orientate. Pentru reprezentarea grafurilor orientate se poate folosi : Matricea de adiacenta ; Matricea varfuri-arce ; Liste de adiacenta ; Vectorul de arce ;. Matricea de adiacenta

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Reprezentarea grafurilor orientate

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  1. Reprezentareagrafurilor orientate

  2. Pentrureprezentareagrafurilor orientate se poatefolosi: • Matricea de adiacenta; • Matriceavarfuri-arce; • Liste de adiacenta; • Vectorul de arce;

  3. Matricea de adiacenta Pentru un graf cu n varfuri , matricea de adiacentaestepatratica,nesimetrica ,ale careielemente se definescastfel: aij=.. • 1, dacaexista arc de la i la j (i,j); • 0, daca nu exista arc de la i la j ; 0 0 1 1 0 0 0 0 0 0 A= 0 1 0 0 0 0 0 1 0 0 1 0 0 1 0 1 2 5 3 4

  4. Vectorul de muchii 1 2 4 3 Pentru un graf cu n varfurisi m arce , vectorul de arce are ca numar de componentevaloarea m . Fiecare element al saufiind un arc care vareprezentaextremitateainitialasiceafinala. V={(1,2),(1,3),(2,3), (4,1),(4,2)}

  5. Matriceavarfuri-arce Se face printr-o matriceB,cu n linii (-varfuri) si m coloane(-arce),in care componentaestereprezentataastfel :bij= • 1 , dacavarfuliesteextremitateinitiala a arculuiUj; • -1, dacavarfuliesteextremitatefinala a arculuiUj; • 0, daca nu existaarcul;

  6. V={(1,2),(1,4),(2,3),(2,5),(3,1),(4,3),(5,4)} u1 u2 u3 u4 u5 u6 u7 1 1 0 0 -1 0 0 -1 0 1 1 0 0 0 B= 0 0 -1 0 1 -1 0 0 -1 0 0 0 1 -1 0 0 0 -1 0 0 1 1 2 4 5 3

  7. Liste de adiacenta Pentrufiecarevarf se construiescdoualiste : • L+(x) : reprezintalistavecinilorsuccesori care continevarfurilecesuntextremitatile finale ale arcelor care ies din varful x; • L-(x) : reprezintalistavecinilorpredecesori care continevarfurilecesuntextremitatileinitiale ale arcelor care intra in varful x;

  8. 1 5 3 4 2

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