Question

Given below is information about a network.

Choose one of the following three​ options:
A. the network is definitely a​ tree;
B. the network is definitely not a​ tree;
C. the network may or may not be a tree​ (more information is​ needed).

Accompany your answer with a brief explanation for your choice. The network has 11 vertices and 11 edges.

Answer 1

Option (B) is the correct answer.

Step-by-step explanation:

The network is used to share the information between two or more persons or systems in a connected pair. It has vertices and edges on which vertices mean the points which participate to communicate and edges are used for the medium by which communication is done.

The network can make the shape of a tree or not. If it follows the property of a tree we can say that it is a tree otherwise it can not be called a tree.

Here in the question, it is a given that there are 11 vertices and 11 edges.

But from the tree property if there are n vertices and n-1 edges then any circuit is called a tree, But this circuit has n edges and n vertices that's why it is not a tree. Hence option b is the correct answer.

While other is not valid because-

• Option "a" suggests that this circuit is a tree that is not correct.
• Option b suggests that this circuit may or may not a tree but it is proved that this circuit is not a tree.