Relevant Definitions

• Weight – The weight of a graph is the sum of all the edges of that graph
• Spanning tree – A subset of a graph which connects all the vertices together
• Minimal Spanning Tree – A subset of a graph which connects all the vertices together and has a weight less than or equal to any spanning tree
• Circuit – A circuit is a path whose first and last vertices are the same

Procedure

Example

Produce the minimal spanning tree for the following graph

Step 1. Sort the edges into the table

Step 2 and 3

• By step 3, As we have n = 5 vertices in the original graph we can stop the process when we have n – 1= 4 chosen edges (i.e. 4 Y’s in the table)

The following minimal spanning tree is obtained

#include <stdio.h>
int main(int argc, char *argv[]) {
    printf("Hello World!\n");
    return (0);
}