Comp 163-002, Spring 2020, MWF, 12:35-1:25, no fixed abode
Week 12 starts Monday, April 6.
The primary goal of this course is to become familiar with some of the
basic mathematical ideas used in programming.
Monday: graph isomorphism
Levin p 234: graph equality and the three drawings of the {a,b,c,d} graph
Example 4.1.1: G1 and G2 are not equal. However, they are isomorphic.
Example 4.12: V1 = {{a,b,c}, {{a,b}, {a,c}, {b,c}}}, V2 = {{u,v,w}, {{u,v}, {u,w}, {v,w}}}
The isomorphism is a→u, b→v, c→w.
Example 4.1.3, p 236: harder, as there is no "obvious" isomorphism. The best approach is to draw them, and compare them visually.
Subgraphs, and example 4.1.4
Dr Sarada Herke, Univ of Queensland, AU, graph-theory Youtube: youtube.com/watch?v=z-GfKbzvtBA
Trees: A tree is a connected graph with no cycles.
Though most of the rest of computer science uses the word "tree" in the sense of something like the following binary search tree:
6
/ \
/ \
4 9
/ \
/ \
2 5
8 37
It has an ordering based on levels.
5
8
| |
2---4---6---9---37
Wednesday: discussion of homework
Subgraphs and induced subgraphs
4.2 Investigate! Spanning trees
Proposition 4.2.3
Proposition 4.2.4: for trees, e=v-1
