A Graph is a non$-$linear data structure consisting of nodes and edges. The nodes are sometimes

also referred to as vertices and the edges are lines or arcs that connect any two nodes in the graph.

Graphs are used to solve many real$-$life problems. Graphs are used to represent networks. The

networks may include paths in a city or telephone network or circuit network. Graphs are also used

in social networks like LinkedIn, Facebook. For example, in Facebook, each person is represented

with a vertex $($or node$).$ Each node is a structure and contains information like person id$,$ name,

gender, locale etc.

Using the graph data table below, complete the required tasks as directed:

Required:

Construct the undirected graph. City $1$ is the source vertex.

Using Bellmaford Algorithm Find the single source shortest path $-$ list the vertices.

Show all possible working.

b$.$ Draw the single source shortest path.

c$.$ What is the total cost of travelling from City $1$ to City $9?$

Using Prim's Algorithm: a$.$ Find the minimum cost spanning tree $-$ list the vertices. Show all

possible working.

b$.$ Draw the minimum spanning tree

c$.$ Calculate the minimum cost

Using Kruskal's Algorithm: a$.$ Find the minimum cost spanning tree $-$ list the vertices. Show all

possible working.

b$.$ Draw the minimum spanning tree

c$.$ Calculate the minimum cost