Homework 5
Graphs
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<FirstName>_<LastName>_ HW5.doc
Problem 1:
[20]
Define the following terms and differentiate between the pairs.
Also, draw a figure illustrating each term.
a) Directed Graph and Undirected Graph
b) Path and Simple Path
c) Cycle and Simple Cycle
d) Spanning Tree and Minimum Spanning Tree
Problem 2:
[20]
Let
G
be a graph whose vertices are the integers 1 through 8, and let the adjacent vertices of each vertex
be given by the table below:
Vertex
Vertex
Vertex
Vertex
Adjacent Vertices
Adjacent Vertices
Adjacent Vertices
1
(2,4)
2
(1,3,4)
3
(2,4)
4
(1,2,3,6)
5
(6,8)
6
(4,5,7)
7
(6,8)
8
(5,7)
Assume that, in a traversal of
, the adjacent vertices of a given vertex are returned in the same order they
are listed in the above table.
a) Draw
G
[4]
b) Order the vertices as they are visited in a depthfirst traversal starting at vertex 1 [8]
c) Order the vertices as they are visited in a breadthfirst traversal starting at vertex 1 [8]
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 Spring '10
 Tessier
 Graph Theory, Vertex, air travel, Adjacency list, adjacent vertices, distance2 neighbors

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