Question

A graph may be defined as a set of points connected by lines called edges. Every edge connects a pair of points. Thus, a triangle is a graph with 3 edges and 3 points. The degree of a point is the number of edges connected to it. For example, a triangle is a graph with three points of degree 2 each. Consider a graph with 12 points. It is possible to reach any point from any point through a sequence of edges. The number of edges, e, in the graph must satisfy the condition

• A. 11≤e≤66
• B. 10≤e≤66
• C. 11≤ e≤ 65
• D. 0≤e≤11

Answer 1

The correct option is A

11≤e≤66

the question is basically asking us to find out the minimum number and maximum number of lines that can be drawn using 12 points.
We can draw a minimum of 11 lines. We can visualize this as one central point and all lines connecting to this point i.e. one point has a degree of 11 and the other 11 have a degree of 1.
There can be a maximum of ${}^{12}$C${}_2$ lines that can be drawn= 66