Generation of acyclic biological diagrams

TL;DR

This paper introduces a novel graph-theoretical method for generating acyclic biological diagrams using permutations related to Motzkin and Dyck paths, aiding biological problem analysis.

Contribution

It presents a new approach linking acyclic biological diagrams to permutations of Motzkin and Dyck paths, offering a fresh perspective for biological diagram generation.

Findings

Defines relative diagrams of cyclic permutations with special vertices.

Establishes a relation between two types of diagrams via permutations.

Potential applications in biological problem analysis.

Abstract

For the generation of acyclic biological diagrams, from a graph-theoretical perspective, we introduce the relative diagrams of cyclic permutations with ramphoid and keratoid vertices of degree 2, which correspond to Motzkin and Dyck words/paths. The relation between these two types of diagrams, defines the generation of the first via the permutations of the second, which may be of assistance in the study and treatment of several biological problems.