Retracting 1-simplicial chaotic graphs with density variation

Abstract EN

In this paper we will discuss retraction transformation on chaotic graphs for different cases of density variation, two types of retraction will be discussed, geometric retraction and chaotic edges retraction, we shall study and discuss the effects of retraction on the shape and density degree of chaotic graphs shown on figures, the adjacent and incidence matrices with be presented.

the density character may present many applications in life such as degree of green color in plants, net perturbation resonance, signals in the nerve system and so many, we focus our study on plants, how retraction effects of the degree of green color of plants leaves and shape of the leave its self.

the variation of the density character shows the variation of the degree of green color of plant (i.e.

chlorophyll), so we divided in three cases, the first case when the leave of plant is unit and constant everywhere, or varied from level to level or varied even in the same level line of a plant leave, each case will be discussed for two types of retraction and deduce results for both types.