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Discreet Mathematics Chapter 5 Graph

Learn about graph theory, types of graphs like simple and directed, representations through matrices and lists, and applications in diverse areas like networking and resource management.

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Discreet Mathematics Chapter 5 Graph

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  1. Discreet MathematicsChapter 5 Graph (Slides adapted from Suzan Hassan)

  2. Graph are Everywhere Graph representation also widely used for problems in such diverse areas as • Road Graph / networks • Railway Graph / networks • Airline traffic Graph / networks • Electrical Graph/ networks, • resource management • financial planning. Definitions -Graph Representation: Graph G =(V, E) consists set of vertices denoted by V, or by V(G) and set of edges E, or E(G)

  3. Edge Type

  4. Graph type

  5. Note: A simple graph is just like a directed graph, but with no specified direction of its edges

  6. Example: V= {u, v, w, k}, E= {{u, w}, {u, v}}solution; deg(u)=2, deg(v)=1, deg(w)= 1, deg(k)= 0 and v are pandant, k is isolated

  7. 1 1 3 3 2 2 4 4 NetworkG = (N, A) Node setN = {1, 2, 3, 4} {(1,2), (1,3), (3,2), (3,4), (2,4)} Arc Set Terminology of Graph Example1: Fined the components of the chart (Degree of Vertis, Cycle and matrix) Solution Cycles: 1, 3, 2, 1 degree 3 3, 4, 2, 3 degree 3 1, 3, 4, 2, 1 degree 4

  8. b 1 2 c a e 4 3 d A Directed Graph The Node-Arc Matrix a b c d e 1234

  9. b 1 2 c a e 4 3 d A Directed Graph Representation of arc lists (for directed graphs) 1: (1,2), (1,4) 2: (2,3) 3:  4: (4,2), (4,3)

  10. b 1 2 c a e 4 3 d An Undirected Graph The Adjacency Matrix (for undirected graphs) 1 2 3 4 degree 1234 2323

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