Overview of Graph Theory lectures:
Lecture 1:
- Definition of graph as a set of vertices and a set of edges (i.e. a relation)
- We talked about the different types of graphs
- directed/undirected
- allow self loops or not
- multigraphs (which need a different representation; set of nodes and set of pairs of nodes is insufficient)
- applications of graph theory
Lecture 2:
- prelim 2 common mistakes
- definition of graph homomorphism (f : V1 -> V2 such that if (u,v) is an edge
in G1 then (f(u), f(v)) is an edge in G2
- definition of isomorphism
Lecture 3:
- paths, connectedness, connected components, strongly connected components,
different equivalent definitions
- course recap
See chapter 10 of Rosen (link on Piazza).