Review on Domination Parameters in Graph Theory with Interdisciplinary Applications
Pallavi Sangolli *
Department of Mathematics, Anuvartik Bharatesh Institute of Technology, Belagavi-590008, Karnataka, India.
Jaishri B. Veeragoudar
Department of Mathematics, KLE Technological University, Dr. M. S. Sheshgiri Campus, Belagavi-590008, Karnataka, India.
*Author to whom correspondence should be addressed.
Abstract
Domination parameters are fundamental graph invariants that capture essential notions such as coverage, control, supervision, and redundancy in complex systems. Among these, the domination number, total domination number, and Roman domination number have received considerable attention due to their wide applicability across diverse domains. In this paper, we present a comprehensive survey and comparative study of these three parameters, focusing primarily on their application-oriented aspects. The work systematically reviews their roles in chemical graph theory, biological systems, and various engineering networks, highlighting their effectiveness as structural descriptors and decision-support tools.
Keywords: Domination, total domination, Roman domination, chemical graph theory, engineering networks