Question 8. A connected graph G has 4 vertices and 4 edges of costs 1, 2, 3 and respectively 4. (a) Show that G is not a tree. (b) Show that G has a single minimum spanning tree. (Hint: For example, think how Prim's algorithm constructs the minimum spanning tree). (c) Draw a connected graph G with 4 nodes and 4 edges of costs 1, 2, 3, 4, respectively, so that the minimum spanning tree contains the edge of cost 4. The 4 nodes are below, you need to draw the 4 edges and indicate their cost. a b d
Question 8. A connected graph G has 4 vertices and 4 edges of costs 1, 2, 3 and respectively 4. (a) Show that G is not a tree. (b) Show that G has a single minimum spanning tree. (Hint: For example, think how Prim's algorithm constructs the minimum spanning tree). (c) Draw a connected graph G with 4 nodes and 4 edges of costs 1, 2, 3, 4, respectively, so that the minimum spanning tree contains the edge of cost 4. The 4 nodes are below, you need to draw the 4 edges and indicate their cost. a b d
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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![Question 8. A connected graph G has 4 vertices and 4 edges of costs 1, 2, 3 and respectively 4.
(a) Show that G is not a tree.
(b) Show that G has a single minimum spanning tree. (Hint: For example, think how Prim's algorithm constructs
the minimum spanning tree).
(c) Draw a connected graph G with 4 nodes and 4 edges of costs 1, 2, 3, 4, respectively, so that the minimum
spanning tree contains the edge of cost 4. The 4 nodes are below, you need to draw the 4 edges and indicate their
cost.
a
O
b
d](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcbf262d4-15d8-4955-836c-ab9ac89afe25%2Fb47bb5a7-946f-41e1-9649-4cfc083a5c6e%2F8x0vyth_processed.png&w=3840&q=75)
Transcribed Image Text:Question 8. A connected graph G has 4 vertices and 4 edges of costs 1, 2, 3 and respectively 4.
(a) Show that G is not a tree.
(b) Show that G has a single minimum spanning tree. (Hint: For example, think how Prim's algorithm constructs
the minimum spanning tree).
(c) Draw a connected graph G with 4 nodes and 4 edges of costs 1, 2, 3, 4, respectively, so that the minimum
spanning tree contains the edge of cost 4. The 4 nodes are below, you need to draw the 4 edges and indicate their
cost.
a
O
b
d
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