Week 14 Euler & Hamiltonian cicuit and path

Question 1

What is this?

• Starts and ends at the same dot.
• Uses every line only once.

Answer 1

Circuit

Question 2

The path D → B → E → G → D → A → B → C → E → H → G → F → D is an ___________

Answer 2

Euler Circuit

Question 3

If it repeats a line or skips one, it’s NOT an ________ circuit.

Answer 3

Euler

Question 4

A graph has an __________Circuit if all the dots have even degrees (an even number of lines attached).

Answer 4

Euler

Question 5

If some dots have 3 or 5 lines, ______ Euler Circuit.

Answer 5

❌ no

Question 6

If all dots have 2, 4, 6, etc. lines, _ Euler Circuit is possible.

Answer 6

✅

Question 7

A _____ is like a route, but it doesn’t need to come back to where it started.

Answer 7

path

Question 8

You can have an Euler Path if:

The graph has exactly _____ dots with an ____ number of lines (odd degrees).

Answer 8

two
odd

Question 9

This time, it’s not about lines, but about dots (vertices)

Answer 9

Hamilton Path and Hamilton Circuit

Question 10

A ________ goes through every dot once and comes back to the start.

Answer 10

Hamiltonian Circuit

Question 11

A _________ goes through every dot once, but doesn’t return to the start.

Answer 11

Hamiltonian Path

Question 12

______→ every line once, ends where you started. All dots have even degrees.

_______ → every line once, starts and ends at different dots. Two dots have odd degrees.

___________ → every dot once, returns to start.

__________ → every dot once, doesn’t return to start.

Answer 12

Euler Circuit
Euler Path
Hamiltonian Circuit
Hamiltonian Path

Question 13

Try walking:
A → B → C → D → A

🎯 You used every line once, and you ended where you started =_________

Answer 13

Euler Circuit

Question 14

Try walking:
B → A → D → C → B → D

🎯 You used every edge once, and you started and ended at the odd-degree dots = _______

Answer 14

Euler Path

Question 15

Now try walking:
A → B → C → D → E → A

🎯 You visited every vertex once and came back = _________

Answer 15

Hamiltonian Circuit

Question 16

A path that contains every vertex of the graph but does not return to the starting point is called _______________

Answer 16

Hamiltonian Path

Question 17

what is this?

Tanan maagian, edges and vertices

Answer 17

Euler

Question 18

A path that contains every vertex of the graph but does not return to the starting point is called _________

Answer 18

Hamiltonian path.

Question 20

every line once, ends where you started. All dots have even degrees.

Answer 20

Euler Circuit

Question 21

every line once, starts and ends at different dots. Two dots have odd degrees.

Answer 21

Euler Path

Question 22

every dot once, returns to start.

Answer 22

Hamiltonian Circuit

Question 23

every dot once, doesn’t return to start

Answer 23

Hamiltonian Path