Applying the Dom-Chromatic Number to Human Gene Regulatory Networks: A Graph-Theoretic Approach to Network Control and Optimization

Abstract

This study introduces the application of the dom-chromatic number from graph theory to human gene regulatory networks (GRNs). The dom-chromatic number quantifies the minimum set of transcription factors required to con- trol a network while covering all functional gene categories. We develop a Python-based algorithm to compute this number efficiently and demonstrate its use in analyzing human GRNs. Our approach offers insights into the opti- mization of gene regulation, with potential applications in synthetic biology, cancer research, and personalized medicine. This work bridges mathematics and biology, providing a novel tool for understanding and controlling gene networks.