Question

Which of these graphs are trees?

Short answer

\(\left( a \right)\)Tree \(\left( b \right)\)Tree \(\left( c \right)\)Not a tree \(\left( d \right)\)Tree \(\left( e \right)\)Not a tree \(\left( f \right)\)Tree.

Step-by-step solution

Definition

A graph is connected if there exists a path between every pair of vertices.

A simple path is a path that does not contain the same edge more than once.

A circuit is a path that begins and ends in the same vertex.

(a)

The given graph is a tree, because the graph is undirected (no arrows on the edges), connected (there exists a path between every pair of vertices) and contains no simple circuits.

(b) Checking whether it is tree or not

The given graph is a tree, because the graph is undirected (no arrows on the edges), connected (there exists a path between every pair of vertices) and contains no simple circuits.

(c) Checking whether it is tree or not

The given graph is a not a tree, because the graph is not connected. For example, there is no path between a and b.

(d) Checking whether it is tree or not

The given graph is a tree, because the graph is undirected (no arrows on the edges), connected (there exists a path between every pair of vertices) and contains no simple circuits.

(e) Checking whether it is tree or not

The given graph is a not a tree, because the graph is not connected. For example, there is no path between a and b.

(f) Checking whether it is tree or not

The given graph is a tree, because the graph is undirected (no arrows on the edges), connected (there exists a path between every pair of vertices) and contains no simple circuits.