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D1 Graphs

D1 Graphs. Faringdon. Barbican. Moorgate. Liverpool St. Chancery Lane. Holborn. St. Pauls. Aldgate. Bank. Node (or vertex). Arc (or edge). Region. Loop. Arc (or edge). Region. Loop. Node (or vertex). Arc (or edge). Region. Loop. Node (or vertex). Arc (or edge). Loop.

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D1 Graphs

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  1. D1 Graphs

  2. Faringdon Barbican Moorgate Liverpool St. Chancery Lane Holborn St. Pauls Aldgate Bank

  3. Node (or vertex) Arc (or edge) Region Loop

  4. Arc (or edge) Region Loop Node (or vertex)

  5. Arc (or edge) Region Loop Node (or vertex)

  6. Arc (or edge) Loop Region Node (or vertex)

  7. Arc (or edge) Loop Region Node (or vertex)

  8. The degree (or valency or order) of this node is 4 Arc (or edge) Loop Region Node (or vertex)

  9. A path is a finite sequence of edges such that the end of one edge is the start of the next and in which no vertex appears more than once.

  10. A path is a finite sequence of edges such that the end of one edge is the start of the next.

  11. A cycle (or circuit) is a closed path, i.e. a path in which the start point is the end point.

  12. A cycle (or circuit) is a closed path, i.e. a path in which the start point is the end point.

  13. A Hamiltonian cycle is a cycle which passes through every vertex of the graph once and only once.

  14. A Hamiltonian cycle is a cycle which passes through every vertex of the graph once and only once.

  15. An Eulerian cycle is a cycle which includes every edge exactly once.

  16. An Eulerian cycle is a cycle which includes every edge exactly once.

  17. An Eulerian cycle is a cycle which includes every edge exactly once.

  18. An Eulerian cycle is a cycle which includes every edge exactly once.

  19. An Eulerian cycle is a cycle which includes every edge exactly once.

  20. An Eulerian cycle is a cycle which includes every edge exactly once.

  21. An Eulerian cycle is a cycle which includes every edge exactly once.

  22. An Eulerian cycle is a cycle which includes every edge exactly once.

  23. An Eulerian cycle is a cycle which includes every edge exactly once.

  24. An Eulerian cycle is a cycle which includes every edge exactly once.

  25. An Eulerian cycle is a cycle which includes every edge exactly once. Not always possible.

  26. A subgraph of G is a graph whose nodes and vertices all belong to G.

  27. A subgraph of G is a graph whose nodes and vertices all belong to G. So, if this is G…

  28. A subgraph of G is a graph whose nodes and vertices all belong to G. Then this is an example of a subgraph of G.

  29. Two vertices are connected if there is a path between them. A E C G B F D

  30. Two vertices are connected if there is a path between them. A E C G B F D So A and C are connected.

  31. Two vertices are connected if there is a path between them. A E C G B F D but A and F are not connected.

  32. A graph is connected if all the vertices are connected. A E C B D

  33. A simple graph is one with no loops or multiple arcs (more than one arc between a pair of vertices). A E C B D

  34. A simple graph is one with no loops or multiple arcs. A E C B D So this graph is not simple because of the loop.

  35. A simple graph is one with no loops or multiple arcs. A E C B D So this graph is not simple because of the loop. and the multiple arcs between A and B.

  36. A simple graph is one with no loops or multiple arcs. A E C B D However this graph is simple.

  37. A weighted graph is a graph with values assigned to the arcs. 5 4 3 4 3 1 6 1 3

  38. A digraph is a graph with directed edges.

  39. A tree is a graph with no cycles. so this is not a tree.

  40. A tree is a graph with no cycles. but this is.

  41. A spanning tree is tree which includes all vertices.

  42. A complete graph is one in which every vertex is joined to every other vertex.

  43. A complete graph is one in which every vertex is joined to every other vertex.

  44. A complete graph is one in which every vertex is joined to every other vertex. This graph is called K5

  45. A bipartite graph is one in which the vertices can be divided into two sets and no pair of vertices within a set are joined.

  46. A complete bipartite graph is one in which every vertex in the first set is joined to every vertex in the second set.

  47. A complete bipartite graph is one in which every vertex in the first set is joined to every vertex in the second set. This graph is called K4,3

  48. A planar graph is one in which can be drawn in 2D with no arcs meeting except at a node.

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