On the Existence of Fault-tolerant numbers of Two-Bridge Knots

Abstract

In this write-up, we explore the family of two-bridge knots for fault-tolerance. We findout fault-tolerant unknotting numbers for certain subfamilies of two-bridge knots. Besidesthis, we work out on special subfamilies C(a, a1, a2, a3, . . . ,±2,−ak,−ak−1, . . . ,−a2,−a1)and C(2n, 3) of two-bridge knots with unknotting number 1 and n respectively and found avarient of fault-tolerant unknotting number called restricetd fault-tolerant unknotting number.Lastly, this paper is concluded by explicating biological disposition of fault-tolerantunknotting number in terms of enzyme action on DNA.