7 - Graphs

Question 1

What is a “complete” graph?

Answer 1

When every vertex is connected to every other vertex by exactly one edge

Question 2

What is a “simple” graph

Answer 2

Has no multiple edges and no vertex is joined to itself

Question 3

What is a “connected” graph?

Answer 3

When all pairs of vertices are connected

Question 4

What is a “subgraph”?

Answer 4

A graph formed by using only some of the edges of the original graph

Question 5

What is a “tree” graph?

Answer 5

connected graph for which it is not possible to find a sequence of distinct edges that returns to the starting vertex

Question 6

What is a “walk”?

Answer 6

Sequence of adjacent edges

Question 7

What is a “trail”?

Answer 7

Walk with no repeated edges

Question 8

What is a “path”?

Answer 8

Walk with no repeated vertices

Question 9

What is a “cycle”?

Answer 9

Walk that starts and ends at the same vertex and has no other repeated vertices

Question 10

What is a “circuit”?

Answer 10

Walk that starts and ends at the same vertex and has no repeated edges

Question 11

What is the differences between a cycle and a circuit?

Answer 11

Both:
- a Walk
- Start and end at same vertex

Difference:
- Cycle has no repeated vertices
- Circuit has no repeated edges