Trees

• A tree is a connected graph where each edge is a bridge.
• We use trees to represent many things, including
  • Family Relationships
  • 
  • Network connections in a local network.
• A spanning tree is a tree that is created from another graph by removing edges while still maintaining a path to each vertex.
  • A graph represents who will calls whom within a department.
  • A spanning tree would be who calls whom in the case of an emergency.
  • Each person is called by one person, except for the department chair.
  • Given this graph:
  • Build this tree:
  • What if we wanted to "Enclose" walkways across campus?
• A minimal spanning tree is the least expensive spanning tree for a given weightd graph.
• Kruskal's Minimal Spanning Tree Algorithm
  1. Select the lowest-cost edge on the graph, add this to the MST
  2. While not all nodes are part of the MST
  3.     Select the next lowest cost edge that does not form a circuit with other verticies in the MST and add this to the MST
• Do problems 9,11,17, 19, 22, 25, 30, 31