If a graph have 12 vertices and 3 connected components, then the largest number of edges it might have is 45.
What is vertex?
One of the items joined together in a graph is referred to as a vertex (or node). Edges or links are the connections between the vertices in any graph.
As given in the question,
The vertices (n) = 12,
Connected components (k) = 3
let m be the number of edges it the graph might have,
The number of edges in the graph can be calculated by the following formula:
[tex]m \le \frac{(n-k+1) \times (n-k)}{2}[/tex]
putting the values from the question,
[tex]m \le \frac{(12-3+1) \times (12-3)}{2}[/tex]
[tex]m \le \frac{(10) \times (9)}{2}[/tex]
[tex]m \le 45[/tex]
By the above equation, we can say that maximum number edges of is 45.
To know more about vertex, go to link
https://brainly.com/question/525947
#SPJ4
