Unit 3 - Graph Theory

Which of the following is a property of a tree?

• It contains cycles

• It is disconnected

• It has n-1 edges for n vertices

• It has more than one component

What is a pendant vertex in a tree?

• A vertex with degree 1

• A vertex with degree 0

• A vertex with highest degree

• A central vertex

In a tree, the number of edges is always:

• Equal to the number of vertices

• Greater than the number of vertices

• One less than the number of vertices

• Twice the number of vertices

The center of a tree is the vertex:

• With maximum degree

• With minimum eccentricity

• That is a leaf

• Farthest from root

A rooted tree has:

• No root

• All vertices as roots

• One designated root

• Only leaves

The eccentricity of a vertex in a tree is:

• Its degree

• The number of leaves

• Maximum distance from that vertex to any other

• Minimum degree in the graph

Which of the following always includes a pendant vertex?

• A cycle

• A complete graph

• A disconnected graph

• A tree with more than one vertex

In a rooted tree, the root is:

• Always a leaf

• A node with no parent

• A node with maximum degree

• A node at the bottom

What is the distance between two adjacent vertices in a tree?

• 1

• 0

• n - 1

• Undefined

A binary tree is a tree in which:

• Each node has exactly two children

• Each node has at most two children

• It has only one leaf

• It is always complete