An algorithm to prescribe the configuration of a finite graph

TL;DR

This paper introduces algorithms using edge slides to transform and regularize connected simple graphs into desired configurations and minimized energy states in finite steps.

Contribution

It presents novel algorithms for graph reconfiguration and regularization through edge slides, enabling controlled evolution to specific structures.

Findings

Algorithms successfully transform graphs into target configurations.

Regularization minimizes energy functional effectively.

Finite-step convergence demonstrated.

Abstract

We provide algorithms involving edge slides, for a connected simple graph to evolve in a finite number of steps to another connected simple graph in a prescribed configuration, and for the regularization of such a graph by the minimization of an appropriate energy functional.