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CSE331 Lecture 11

# CSE331 Lecture 11 - n vertices HW 2 due today Q1 Q2 and Q3...

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Lecture 11 CSE 331 Sep 23, 2011

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HW 2 due today 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

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HW 3 Has been posted (link on the blog) Start early
Graded HW 1 Pick up from recitation/TA office hours next week

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Graphs Representation of relationships between pairs of entities/elements Vertex Vertex Edge Edge # vertices = n #edges = m # vertices = n #edges = m
Paths Sequence of vertices connected by edges , , , Path length 3 Path length 3 , Connecte d Connecte d

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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

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

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

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Unformatted text preview: n vertices? HW 2 due today 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 A rooted tree Pick any vertex as root Let the rest of the tree hang under “gravity” How many rooted trees can an n vertex tree have? How many rooted trees can an n vertex tree have? SG’s parent=AC SG’s parent=AC AC’ s chil d=S G AC’ s chil d=S G Rest of Today’s agenda Prove n vertex tree has n-1 edges Algorithms for checking connectivity Checking by inspection What about large graphs? s t Are s and t connected? Brute-force algorithm? List all possible vertex sequences between s and t Check if any is a path between s and t n n such sequences n n such sequences Algorithm motivation al l al l...
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CSE331 Lecture 11 - n vertices HW 2 due today Q1 Q2 and Q3...

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