4. Let G=(V, E) be the following undirected graph: V = {1, 2, 3, 4, 5, 6, 7, 8} E = {(1, 7) (1, 4), (1, 6), (6, 4), (7, 5), (2, 5), (2, 4), (4, 3), (4, 8), (8, 3), (3,5)}. a. Draw G. b. Is G connected? c. Give the adjacency matrix for the graph G given above. d. Determine whether the graph has a Hamiltonian cycle. If the graph does have a Hamiltonian cycle, specify the nodes of one. If it does not, prove that it does not have one. e. Determine whether the graph has a Euler cycle. If the graph does have a Euler cycle, specify the nodes of one. If it does not, prove that it does not have one.
4. Let G=(V, E) be the following undirected graph: V = {1, 2, 3, 4, 5, 6, 7, 8} E = {(1, 7) (1, 4), (1, 6), (6, 4), (7, 5), (2, 5), (2, 4), (4, 3), (4, 8), (8, 3), (3,5)}. a. Draw G. b. Is G connected? c. Give the adjacency matrix for the graph G given above. d. Determine whether the graph has a Hamiltonian cycle. If the graph does have a Hamiltonian cycle, specify the nodes of one. If it does not, prove that it does not have one. e. Determine whether the graph has a Euler cycle. If the graph does have a Euler cycle, specify the nodes of one. If it does not, prove that it does not have one.
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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![4. Let G=(V, E) be the following undirected graph:
V = {1, 2, 3, 4, 5, 6, 7, 8}
E = {(1, 7) (1, 4), (1, 6), (6, 4), (7, 5), (2, 5), (2, 4), (4, 3), (4, 8), (8, 3), (3, 5)}.
a. Draw G.
b. Is G connected?
c. Give the adjacency matrix for the graph G given above.
d. Determine whether the graph has a Hamiltonian cycle. If the graph does have
a Hamiltonian cycle, specify the nodes of one. If it does not, prove that it does
not have one.
e. Determine whether the graph has a Euler cycle. If the graph does have a Euler
cycle, specify the nodes of one. If it does not, prove that it does not have one.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa88f04d6-da61-4171-acd5-bf998d4872ea%2F4ffa17b1-34fb-4aa3-948b-4968c484c4ce%2Fhk76k_processed.png&w=3840&q=75)
Transcribed Image Text:4. Let G=(V, E) be the following undirected graph:
V = {1, 2, 3, 4, 5, 6, 7, 8}
E = {(1, 7) (1, 4), (1, 6), (6, 4), (7, 5), (2, 5), (2, 4), (4, 3), (4, 8), (8, 3), (3, 5)}.
a. Draw G.
b. Is G connected?
c. Give the adjacency matrix for the graph G given above.
d. Determine whether the graph has a Hamiltonian cycle. If the graph does have
a Hamiltonian cycle, specify the nodes of one. If it does not, prove that it does
not have one.
e. Determine whether the graph has a Euler cycle. If the graph does have a Euler
cycle, specify the nodes of one. If it does not, prove that it does not have one.
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