Application of Discrete Mathematics in Groundwater Quality Assessment: A Case Study from Rahata Tehsil, Ahilyanagar District, Maharashtra, India

Abstract

Discrete mathematics offers powerful analytical tools for modeling and evaluating environmental data, particularly in scenarios involving classification, relational analysis, and pattern enumeration. This study demonstrates the application of set theory, graph theory, and combinatorics to assess groundwater quality parameters from 34 samples (17 tube wells and 17 open wells) collected across 17 villages in Rahata Tehsil, Ahmednagar District, and Maharashtra. Key hydro chemical parameters analyzed include pH, electrical conductivity (EC), major ions (Ca²⁺, Mg²⁺, Na⁺, K⁺, HCO₃⁻, Cl⁻, SO₄²⁻), total dissolved solids (TDS), and total hardness. Data discretization enables set-based classification of quality levels, graph-theoretic analysis reveals parameter interdependencies through correlation networks, and combinatorial methods quantify multi-parameter exceedance patterns against Bureau of Indian Standards (BIS IS 10500:2012) drinking water specifications. Results demonstrate strong graph connectivity among salinity-related parameters (EC, TDS, Mg²⁺, Na⁺) with Pearson correlation coefficients exceeding 0.8, indicating geogenic linkages characteristic of basaltic aquifer weathering. Thirty samples (88%) exceeded TDS acceptability limits of 500 mg/L, while combinatorial analysis identified two samples with extreme multi-parameter violations. These discrete mathematical approaches provide a structured, computationally efficient framework for identifying groundwater quality hotspots and supporting sustainable water resource management in semi-arid basaltic terrains.