Deck 14: Available Online: Other Mathematical Systems

Question 1

A) The graph is not a tree because two edges overlap.
B) The graph is not a tree because it is disconnected.
C) The graph is not a tree because it contains a circuit.
D) The graph is a tree.

Answer 1

B

Question 2

A) F, D, C, B, A, E, D, F
B) E, B, A, D, F, C, E
C) A, E, B, C, F, D, E, A
D) F, D, E, A, B, C, F

Answer 2

D

Question 3

A) Euler path: C-B-A-H-G-I-J-F-E-D-C-F
B) Euler circuit: B-A-H-G-B-C-D-E-F-G-I-J-F-C-B
C) Euler path: B-A-H-G-B-C-D-E-F-G-I-J-F-C
D) neither exists

Answer 3

C

Question 4

A) The graph is not a tree because it contains a circuit.
B) The graph is not a tree because two edges overlap.
C) The graph is not a tree because it is disconnected.
D) The graph is a tree.

Question 5

A) Euler path: A, B, C, D, E, F, G, H, C, A, H
B) Euler circuit: A, B, C, D, E, F, G, H, A
C) Euler path: A, B, C, D, E, F, G, H, A
D) neither

Question 6

A) 255 miles
B) 249 miles
C) 215 miles
D) 224 miles

Question 7

A) 304
B) 238
C) 213
D) 303

Question 8

Decide whether the connected graph has an Euler path, an Euler circuit, an Euler circuit butnot an Euler path, or neither an Euler circuit nor an Euler path. The graph has 2 odd vertices and 2 even vertices.

A) Euler circuit but not an Euler path
B) Euler path
C) neither an Euler circuit nor an Euler path
D) Euler circuit

Question 9

Decide whether the connected graph has an Euler path, an Euler circuit, an Euler circuit butnot an Euler path, or neither an Euler circuit nor an Euler path. The graph has 4 odd vertices and 5 even vertices.

A) Euler circuit
B) Euler circuit but not an Euler path
C) neither an Euler circuit nor an Euler path
D) Euler path

Question 10

Question 11

A) B, C
B) A, B, C, D, E, F
C) A, D, E, F
D) A, D

Question 12

Question 13

Find the number of Hamilton circuits if a complete graph has five vertices.

A) 24
B) 32
C) 720
D) 120

Question 14

A) 4
B) 6
C) 7
D) 1

Question 15

A) 243 miles
B) 227 miles
C) 255 miles
D) 258 miles

Question 16

A) 246
B) 209
C) 221
D) 249

Question 17

A) The graph is not a tree because it contains a circuit.
B) The graph is a tree.
C) The graph is not a tree because two edges overlap.
D) The graph is not a tree because it is disconnected.

Question 18

A) C, D, A, B, C
B) C, D, F, C
C) C, D, A, B
D) C, D, F, D, C

Question 19

Question 20

A) EF and EH
B) GH and FG
C) GH and HI
D) HI and FI

Question 21

A) neither
B) Euler circuit: A, B, C, D, E, F, D, G, H, C, A
C) Euler path: H, C, A, B, C, D, E, F, D, G
D) Euler path: H, C, A, B, C, D, E, F, D, G, H, G

Question 22

Question 23

A) F, D, C, B, A, E
B) D, E, A, B, C, D, F
C) F, D, A, B, C, E
D) E, A, D, C, B, A, D, F

Question 24

A) 172 feet
B) 176 feet
C) 181 feet
D) 192 feet

Question 25

A) AE, BC, DF
B) A, D
C) AE, DF
D) E, F

Question 26

A) A, F
B) A, B, C, D
C) B, C, D, E
D) A, B, C, D, E, F

Question 27