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In this paper introduces and investigates the Randic index for unclear graphs and neutrosophic subgraphs. It effective models in uncertainty and imprecision in edge and vertex relations. This study examines the Randic index’s features for neutrosophic graphs and the impact of isomorphism between graphs. Furthermore, the notion is extended to directed neutrosophic graphs, offering a novel approach to analysing directed structures under uncertainty. The Randic index can help determine the best site for a waste management plant, as demonstrated in a real-world example. This approach emphasises the Randic index’s practical importance in urban planning and infrastructure development, demonstrating its larger impact across several disciplines.
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