Understanding Trees in Graph Theory

The video tutorial explains the concept of trees in graph theory, highlighting that a tree is a connected, acyclic graph where the number of edges equals the number of vertices minus one. The tutorial examines four graphs (A, B, C, and D) to determine if they are trees. Graph A is not a tree because it has too many edges. Graph B is a tree as it meets all criteria. Graph C is also a tree, being connected and acyclic. Graph D is not a tree due to insufficient edges. The video emphasizes checking both the edge-vertex relationship and the graph's connectivity and acyclic nature.

What is a tree in graph theory?

• A connected graph with no cycles

• A graph with cycles

• A disconnected graph

• A connected graph with cycles

Which equation must hold true for a graph to be a tree?

• e = v / 2

• e = v + 1

• e = v - 1

• e = v * 2

Why is graph A not considered a tree?

• It has more vertices than edges

• It is not connected

• It has cycles

• The equation e = v - 1 does not hold

What characteristic of graph B confirms it as a tree?

• It is disconnected

• It has cycles

• It has more edges than vertices

• It satisfies e = v - 1 and is connected with no cycles

How many edges does graph B have?

• Four

• Five

• Six

• Three

What makes graph C a tree?

• It satisfies e = v - 1 and is connected with no cycles

• It is not connected

• It has more edges than vertices

• It has cycles

How many vertices does graph C have?

• Six

• Three

• Four

• Five

Why is graph D not a tree?

• It is not connected

• It has more edges than vertices

• It has cycles

• The equation e = v - 1 is not satisfied

How many edges does graph D have?

• Two

• Three

• Five

• Four

What is the key condition for a graph to be a tree?

• It must have more edges than vertices

• It must have cycles

• It must be disconnected

• It must be connected and acyclic