If we consider to be a connected graph, with and , then has been defined as the distance between a vertex and an edge . The cardinality of the smallest subset which can assign a unique distance vector to every edge of is referred to as edge metric dimension (EMD) given by . A multiwheel graph is composed of cycles along with a central vertex such that is adjacent to each of the vertices of and the corresponding vertices of the two consecutive cycles and are also adjacent for all . This article discusses the EMD of the double wheel graph and extends the results to the general multiwheel graph.
"Edge metric dimension of $k$ multiwheel graph." Rocky Mountain J. Math. 50 (4) 1175 - 1180, August 2020. https://doi.org/10.1216/rmj.2020.50.1175