We have known that the polygonal index of a tame knot is a knot invariant. In this thesis, we show that every nontrivial knot has polygon index not smaller than 6 and give some estimations of the polygon indices of torus knots $T_{r,s}$, whitehead doubles of the unknot having n crossings $W_n$, pretzel links $Sigma(a_1, a_2$,…,$a_n$) and connected sums p#$\iota$."
본 논문에서는 매듭 불변량인 Polygon Index에 대해서 다음과 같은 성질을 연구하였다.
1. Every nontrivial knot has polygon index not smaller than 6.
2. 2 $min{2r, s} \le p(T_{r,s}) \le r min{n|n > \frac{2s}{r}$.
3. $p(W_n) \le n+3$.
4. $p(\Sigma(a_1,a_2$,…,$a_n)) \le n+\displaystyle\sum_{i=1}^n|a_i|$.
5. $p(k#1) \le p(k)+p(1)-2$.
