Day 16: mat385

Today: Dr. Don Krug makes a special guest appearance

• Collect homework 5.1

• Start Section 5.2: Trees and their representations

  Trees and tree-like graphs appear in funny places: I was listening to NPR (3/13/05) and Will Short, the Puzzle Guy, gave this puzzle:

  		W
  	A		I
  R		G		T

  This is a graph like the Hexstat probability generator (draining from top to bottom): connected, directed, acyclic. Let's turn it into a tree, by duplicating some nodes:

  		W
  A				I
  R		G		G		T

  In traversing this graph from root to leaf, in four possible ways, every way spells out a word: WAR, WAG, WIG, WIT; he asked us to create a tree of depth 3 that uses the ten letters in ANALOGIES+K and does the same thing.... (as a hint, he said that an A is the left-most leaf, only not in those those words!).

Links:

• A friendly glossary of graph terminology

• NIST (the National Institute of Standards and Technology) defines it as "A connected, undirected, acyclic graph". Our book does not require the "undirected" part, and many sources assume that a tree is directed! This does, unfortunately, add to the confusion.... An ordered tree is one where the children are numbered (there is a left to right), which is important for tree traversal.

• NIST (the National Institute of Standards and Technology) Dictionary of Algorithms and Data Structures

• No need to restrict Euler's formula to simple graphs! If you find a theorem with restrictions, ask yourself why the restrictions are there! (Now: is connectedness important?)