Sect 7. Graphs

CONCEPTS
  
  Graph, node, edge
  Directed, undirected, weighted
  Adjacent, cycle, degree (in/out)
  n-cube, complete, bipartite
  Adiacency matrix, Incidence matrix, Adjiacency list
  Graph isomorphism
  Path, circuit, Euler, Hamilton
  Shortest Path, Dijkstra
  Traversal (breadth/first)
  Minimal spanning tree, Prim, Kruskal
  
NOTATION

SKILLS
  
  1. Identify concepts in a context
     E.g., Tell nodes, arcs, weights, directions in a graph
     E.g., Describe n-cube and complete graphs
     E.g., Compute matrices and lists defining graphs
  2. Manipulate graphs
     E.g., Produce Euler and/or Hamilton paths and/or circuits
     E.g., Execute by hand Dijkstra shortest path algorithms
     E.g., Compute graph traversals 
     E.g., Minimal spanning trees with Prim and/or Kruskal
  3. Use graphs to analyze simple problems
     E.g., build game space of tic-tac-toe
       
SOURCES

  Tutorialspoint: Graph & Graph Models
  https://www.tutorialspoint.com/discrete_mathematics/graph_and_graph_models.htm

  *** Recommended ***
  Wikipedia: Graph (discrete mathematics)
  https://en.wikipedia.org/wiki/Graph_%28discrete_mathematics%29

  Wikibooks: Discrete Mathematics/Graph theory
  https://en.wikibooks.org/wiki/Discrete_Mathematics/Graph_theory

  Wikibooks: Programming Concepts: Graphs
  https://en.wikibooks.org/wiki/A-level_Computing/AQA/Paper_1/Fundamentals_of_data_structures/Graphs

  geeksforgeeks: Dijkstra’s shortest path algorithm
  http://www.geeksforgeeks.org/greedy-algorithms-set-6-dijkstras-shortest-path-algorithm/

  *** Recommended ***
  Youtube: Dijkstra’s Shortest Path Algorithm by Kevin Drumm
  https://www.youtube.com/watch?v=pVfj6mxhdMw

  *** Recommended ***
  Youtube: Graph Traversals - Breadth First and Depth First by Abhinav Tripathi
  https://www.youtube.com/watch?v=bIA8HEEUxZI

  *** Recommended ***
  Youtube: Prim's Algorithm: Minimal Spanning Tree by Barry Brown
  https://www.youtube.com/watch?v=YyLaRffCdk4

  *** Recommended ***
  Youtube: Minimum Spanning Tree #1: Kruskal Algorithm by Bo Qian
  https://www.youtube.com/watch?v=5xosHRdxqHA

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  *** Recommended ***   
  Lerma, chap 7 

  LLM, sect 6.1 and 6.4

  ADS, chap 9 (many exercises)

  BDS, chap 9

  Levin: Chap 4 (extensive)