<![CDATA[This study presents the implementation of the Breadth First Search (BFS) algorithm to determine the dominant local metric dimension on path graphs through a web-based platform. The system allows users to input the number of vertices, generates a corresponding path graph, computes the dominant local metric basis set, and calculates the minimum distance from each vertex to the basis using BFS. All processes are automated and displayed interactively using the Plotly library within a responsive website interface. The system was built using the Django framework, employing NetworkX for graph operations and Plotly for visualization. The BFS algorithm ensures the shortest distance calculation from a starting vertex to all others, providing a unique distance vector for each vertex that satisfies domination and local resolving set properties. This research shows that BFS is not only effective for theoretical computations but also practical in digital applications. Future development is recommended to support more complex graph structures, such as cycles, trees, or general graphs, to enhance the system's versatility.]]>
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