Question

Consider the undirected graph $\mathbf{G}\mathbf{=}\mathbf{(}\mathbf{V}\mathbf{,}\mathbf{E}\mathbf{)}$where$\mathbf{V}$, the set of nodes, is$\mathbf{\{}\mathbf{1}\mathbf{,}\mathbf{2}\mathbf{,}\mathbf{3}\mathbf{,}\mathbf{4}\mathbf{\}}$
and$\mathbf{E}$, the set of edges, is$\mathbf{\left\{}\mathbf{\{}\mathbf{1}\mathbf{,}\mathbf{2}\mathbf{\}}\mathbf{,}\mathbf{\{}\mathbf{2}\mathbf{,}\mathbf{3}\mathbf{\}}\mathbf{,}\mathbf{\{}\mathbf{1}\mathbf{,}\mathbf{3}\mathbf{\}}\mathbf{,}\mathbf{\{}\mathbf{2}\mathbf{,}\mathbf{4}\mathbf{\}}\mathbf{,}\mathbf{\{}\mathbf{1}\mathbf{,}\mathbf{4}\mathbf{\}}\mathbf{\right\}}\mathbf{.}$ Draw the graphG. What are the degrees of each node? Indicate a path from node 3 to node 4 on your drawing ofG.

Short answer

Below is the Graph G,

The degree of each node is as follows:

• Node 1 has degree 3.
• Node 2 has degree 3.
• Node 3 has degree 2.
• Node 4 has degree 2.

The path from node 3 to node 4 is shown below using the blue color:

Step-by-step solution

Describe the steps taken to draw the graph.

1. Draw four circles as the nodes of the graph and number them.
2. Connect nodes with a line for which there is an ordered pair in set E. For instance, (1,2) is given in the set, so make node 1 and node 2 connected.

Describe the degree of each node

A degree can be defined as the number of incoming or outgoing edges to a node.

• There are 3 edges directly linked to nodes 1 and 2, so their degree is 3.
• There are 2 edges directly linked to nodes 3 and 4, so their degree is 2.

Describe the path from node 3 to node 4

A path can be defined as the set of connected edges through which we can reach from one node to another node.

There can be many possible paths from node 3 to node 4, some are as follows:

$\begin{array}{l}3\to 2\to 4\\ 3\to 1\to 4\\ 3\to 1\to 2\to 4\\ 3\to 2\to 1\to 4\end{array}$