Qom University of Technology Mathematics and Computational Sciences 27172708 7 1 2026 02 01 Efficient and resilient metro rail networks through graph domination, connectivity, and coloring methods 104 117 733708 10.30511/mcs.2025.2075308.1535 EN Siddharthan Rajeshkanna Department of mathematics, AMET university, Chennai, India 0009-0002-8700-3636 Kungumaraj Eswarasamy Department of Science and Humanities, Nehru In- stitute of Engineering and Technology, Coimbatore, India 0000-0001-9821-9913 Jenitha Ganesan Department of Mathematics, AMET University, Chennai, India 0000-0002-8008-8836 Journal Article 2025 10 20 The utilization of the Indian rail system has grown at a very high rate and there is one of the largest train track networks in the world in the country. Despite the creation of various sophisticated means of transport, congestion, inefficiency and bad connectivity remain factors to contend with. To overcome these challenges, the metro rail has been<br>discovered to be the most possible urban mass transit system and can be easily modeled using graph theory with vertices represented by stations and edges by tracks. In this paper, we begin by examining traditional metrics like connectivity, complexity, diameter,<br>average distance between the terminals and potential expansion of the network in the hope<br>of quantifying passenger convenience and efficiency. We also advance the research with<br>new concepts: vertex and edge domination are used to compute the minimum critical<br>station for effective surveillance, vertex and edge connectivity to quantify survivability against failure and labeling or coloring techniques for use with scheduling, traffic control and resource allocation. This joint approach results in both classical and new findings for more resilient metro network planning and construction. https://mcs.qut.ac.ir/article_733708_72e75cb58ee3f73c7951dcf479e41dfc.pdf