Permutations and Combinations

Level 2

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 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 other point through a sequence of edges. The number of edges, e, in the graph must satisfy the condition.

10 less than or equal to eless than or equal to 66 0 less than or equal to e less than or equal to 11 11 less than or equal to e less than or equal to 66 11 less than or equal to e less than or equal to 65

1 solution

Nguyen Thanh Long
Jan 31, 2015

Because there is route between any pair of two points, in the worst case there is only one route connecting these points. So this route has 12 point and has 11 edges. In the full connection, any point also has edges connect directly to others points. So there are: $\frac{12 \times 11 }{2}=\boxed{66}$ edges in this graph.

Permutations and Combinations

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