AMS 301.3 (Fall, 2009)
Estie Arkin
Homework Set # 5
Due in class on Monday, October 19, 2009.
Recommended Reading: Tucker, 3.1, 3.2
Do Problems:
Problem A: Let
T
be a balanced 5ary tree with 81 nodes.
(a). How many internal nodes does
T
have?
(b). How many edges does the tree
T
have?
(c). What is the height of
T
?
16, 26(a) — Section 3.1
Problem B: (a). Determine the DFS tree of
K
3
,
3
.
(b). Determine the BFS tree of
K
3
,
3
.
problem C: True or False? If true, give a short proof. If false, give a counterexample:
(a). For any connected graph
G
, all internal nodes of the BFS tree on
G
have the same number of children.
(b). For any connected graph
G
, the DFS tree on
G
and the BFS tree on
G
have the same number of edges.
Homework Set # 6
Due in class on Monday, October 26, 2009.
Recommended Reading: 3.3 (read the introduction on page 113, and then the section “Approximate Traveling
Salesperson Tour Construction”, pages 117120), 4.2, 4.1. Read also the handouts on the web about Dijkstra’s
algorithm and the TSP tour construction.
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 Spring '08
 ARKIN
 Graph Theory, Shortest path problem, node node node, Node Node Node Node Node Node

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