<p>Reliable communication in wireless sensor networks (WSNs) depends on effective sustainable network monitoring. Efficient fault detection mechanisms are essential to sustain optimal performance with minimal resource usage. The monitoring edge geodetic set addresses this need by offering a mathematical approach to minimize monitoring points while guaranteeing complete coverage of network edges. In this paper, we present a novel polynomial-time algorithm to compute the monitoring edge geodetic number for triangular honeycomb networks. We develop specialized computational techniques that exploit the unique structural properties of triangular honeycomb networks to achieve optimal monitoring coverage with minimal resources. Our algorithm demonstrates superior performance with O(n) time complexity compared to existing approaches, and provides exact solutions for networks of dimension n. Experimental validation across networks ranging from dimensions 1 to 100 shows consistent optimal results with execution times under 10ms for large-scale networks. The method demonstrates a reduction of monitoring resources by nearly 40%, yet preserves full edge coverage, thereby proving advantageous for WSNs operating under strict energy and cost limitations.</p>