GATE CSE 1998 | Question: 10a

Question

Prove by induction that the expression for the number of diagonals in a polygon of $n$ sides is $\frac{n(n-3)}{2}$

Answer 1

Part B
m=0 n=15
For first graph R1 repeat itself after a cycle of 3 i.e R1^0=R1^3.
Similarly, R2^0=R2^5
So, both will repeat themselves after LCM(3,5)=15.
Therefore,m=0 and n=15

Answer 2

According to me, for part B,

The digraphs R^n where (n>=5) are all same because they only consist of self-loops. Therefore, the answer is (m,n) = (5,6).

Note: R^n = R^n-1 o R where R^n is called the power of a relation.