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Key Terms

12.1 Graph Basics

  • vertex
  • edge
  • loop
  • graph (simple graph)
  • multigraph
  • adjacent (neighboring)
  • degree

12.2 Graph Structures

  • complete
  • subgraph
  • cycle
  • cyclic subgraph
  • clique

12.3 Comparing Graphs

  • isomorphic
  • isomorphism
  • planar
  • nonplanar
  • complement
  • complementary

12.4 Navigating Graphs

  • walk (directed walk)
  • trail (directed trail)
  • path (directed path)
  • closed
  • open
  • closed walk
  • circuit (closed trail)
  • directed cycle (closed path)
  • coloring (graph coloring)
  • nn-coloring
  • chromatic number

12.5 Euler Circuits

  • connected
  • component
  • disconnected
  • Euler circuit
  • Eulerian graph
  • Chinese postman problem
  • Eulerization

12.6 Euler Trails

  • algorithm
  • Fleury’s algorithm
  • Euler trail
  • bridge
  • local bridge

12.7 Hamilton Cycles

  • Hamilton cycle, or Hamilton circuit
  • nn factorial
  • weighted graph
  • total weight

12.8 Hamilton Paths

  • Hamilton path

12.9 Traveling Salesperson Problem

  • brute force algorithm
  • greedy algorithm
  • traveling salesperson problem (TSP)
  • brute force method
  • nearest neighbor method

12.10 Trees

  • acyclic
  • tree
  • forest
  • path graph or linear graph
  • star tree
  • root
  • starlike tree
  • caterpillar tree
  • lobster tree
  • spanning tree
  • minimum spanning tree
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