The Edge Partition Dimension of Graphs

Abstract

Theedgemetric dimension wasintroduced in 2018 and since then, it has been extensively studied. In this paper, we present a different way to obtain resolving structures in graphs in order to gain more insight into the study of edge resolving sets andresolving partitions. We define the edge partition dimension of a connected graph and bound it for graphs of given order andfor graphswithgivenmaximumdegree. Weobtainexactvaluesoftheedgepartitiondimensionformultipartite graphs. Some relations between the edge partition dimension and partition dimension/edge metric dimension are also presented. Moreover, several open problems for further research are stated.