Smart Monitoring of Urban Feeder Systems via Power Dominator Coloring: A Graph-Theoretic Approach for Chennai Metro

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DOI: https://doi.org/10.28924/2291-8639-24-2026-167
Published: May 29, 2026
Cite as:
G. Navamani, L. Jacquline, Daniel Breaz, Kadhavoor R. Karthikeyan, Smart Monitoring of Urban Feeder Systems via Power Dominator Coloring: A Graph-Theoretic Approach for Chennai Metro, Int. J. Anal. Appl., 24 (2026), 167.

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G. Navamani, L. Jacquline, Daniel Breaz, Kadhavoor R. Karthikeyan

Abstract

Power dominator coloring is a variant of dominator coloring in which every vertex in a graph must power dominate at least one color class in a proper vertex coloring. In this study, we investigate the power dominator chromatic number, denoted by χpd(G), specifically for caterpillar graphs. We establish tight bounds for χpd(G), based on the support vertices along the spine of the caterpillar. Capitalizing on the structural properties of these graphs, such as spine and support vertex distribution, we introduce an efficient algorithm to calculate χpd(G). A linear time implementation of the algorithm using MATLAB is constructed, and its application is illustrated in a case analysis of the Chennai Metro feeder network. The results illustrate effective monitoring and optimal resource allocation, highlighting the practical utility of power dominator coloring in real-world urban transport networks.

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