Question

Given below is information about a network. Choose one of the following three​ options: the network is definitely a​ tree; the network is definitely not a​ tree; 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 15 vertices and no bridges.

Answer 1

A Network is definitely a Tree when any of the below properties matched.

Explanation:

A Network is synonym for connected graph. Connected graph is a graph is a path which will connect from vertex to vertex.

A Tree is a network that has no circuit. network can be differed from tree by three key properties

1. Single path property - one path connecting two vertices

2. All bridges property - every edge of a network is a bridge

3. N-1 edges property - N vertices has N-1 edges

To determine this we use to N-1 edges property as given number of vertices and no bridges.

If a network has 15 vertices it must have 15-1= 14 edges to become a tree