The concept of hairpin structures in formal languages is motivated from the biocomputing and bioinformatics fields. Hairpin (-free) DNA structures have numerous applications to DNA computing and molecular genetics in general. A word is called hairpin-free if it cannot be written in the form , with certain additional conditions, for an involution (a function with the property that equals the ide...

The result involution graph of a finite group , denoted by is an undirected simple whose vertex set the whole and two distinct vertices are adjacent if their product element. In this paper, graphs for all Mathieu groups connectivity in studied. diameter, radius girth also Furthermore, several other properties obtained.

There are three types of involutions on a cubic fourfold; two anti-symplectic type, and one symplectic. Here we show that cubics with exhibit the full range behaviour in relation to rationality conjectures. Namely, general fourfold symplectic involution has no associated<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper K Baseline ...