On the edge metric dimension of some families of splitting graphs

The edge metric dimension is the minimum cardinality of the ordered set of vertices that uniquely identifies each pair of distinct edges of a graph using distance vectors. One of the edge metric dimension applications is image processing and pattern recognition. Splitting graphs have many applications in various fields, including computer network architecture, social network analysis, and transportation planning. [H. Pan, M. Ali, G. Ali, M. T. Rahim and X. Yang, On the families of graphs with unbounded metric dimension, IEEE Access 7 (2019) 165060–165064] computed the metric dimension of the splitting graph of path and cycle, proved that dim[Formula: see text] and dim[Formula: see text] respectively; the result on the splitting graph of the path, particularly when [Formula: see text] was challenged by [H. Raza, Y. Ji and S. Qu, On mixed metric dimension of some path related graphs, IEEE Access 8 (2020) 188146–188153], and an improved result was made on the metric dimension of the splitting graph of the path, and showed that dim[Formula: see text] In this paper, we agree with the results of [H. Pan, M. Ali, G. Ali, M. T. Rahim and X. Yang, On the families of graphs with unbounded metric dimension, IEEE Access 7 (2019) 165060–165064]. We improve their results by providing a metric generator of a smaller order for the splitting graph of the path when [Formula: see text]. [L. Li, S. Bao and H. Raza, On some families of path-related graphs with their edge metric dimension, Examples Counterexamples 6 (2024) 100152] computed the edge metric dimension of the splitting graph of the path, and proved that edim[Formula: see text] for [Formula: see text] we improve the result by providing an edge metric generator of smaller order and showing that edim[Formula: see text] for [Formula: see text] Furthermore, we computed the edge metric dimension of the splitting graph of the cycle. Our results contribute to the families of graph [Formula: see text] achieving equality edim[Formula: see text] = dim[Formula: see text]