Lecture 11 CSE 331 Sep 23, 2011

HW 2 due today I will not take any HW after 1:15pm Q2, Q3 and Q4 in different piles I will not take any HW after 1:15pm

Solutions to HW 2 Handed out at the END of the lecture

HW 3 Has been posted (link on the blog) Start early

Graded HW 1 Pick up from recitation/TA office hours next week

Graphs Representation of relationships between pairs of entities/elements # vertices = n #edges = m Edge Vertex

Paths , , Sequence of vertices connected by edges Connected Path length 3 ,

Connectivity u and v are connected iff there is a path between them A graph is connected iff all pairs of vertices are connected

Connected Graphs Every pair of vertices has a path between them

Cycles Sequence of k vertices connected by edges, first k-1 are distinct ,

Puzzle # 3 How many distinct graphs on n vertices? How many distinct trees on n vertices?

HW 2 due today I will not take any HW after 1:15pm Q1, Q2 and Q3 in different piles I will not take any HW after 1:15pm

Tree Connected undirected graph with no cycles

Rooted Tree

How many rooted trees can an n vertex tree have? A rooted tree How many rooted trees can an n vertex tree have? AC’s child=SG Pick any vertex as root SG’s parent=AC Let the rest of the tree hang under “gravity”

Rest of Today’s agenda Prove n vertex tree has n-1 edges Algorithms for checking connectivity

Checking by inspection

What about large graphs? Are s and t connected?

Brute-force algorithm? List all possible vertex sequences between s and t nn such sequences Check if any is a path between s and t

Algorithm motivation all