Day 16: mat385

Today:

• Return homework 3.1: problems 28 and 34

• Questions on Homework for 5.1?
  • Question from last time:

    where in the proof of Euler's formula (by induction on arcs) was simplicity required?
    (Was it merely accidental that the formula worked for the non-simple graph of figure 5.17, p. 350?)

• Section 5.2: Trees and their representations

Next time: section 5.3: Decision Trees

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?)