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An edge-locating coloring of a simple connected graph G is a partition of its edge set into matchings such that the vertices of G are distinguished by the distance to the matchings. The minimum number of the matchings of G that admits an edge-locating coloring is the edge-locating chromatic number of G, and denoted by χ ′ L (G). This paper introduces and studies the concept of edge-locating coloring. Graphs G with χ ′ L (G) ∈2, m are characterized, where m is the size of G. We investigate the relationship between order, diameter and edge-locating chromatic number. We obtain the exact values of χ ′ L (K n) and χ ′ L (K n − M), where M is a maximum matching; indeed this result is also extended for any graph. We determine the edge-locating chromatic number of the join graphs of some well-known graphs. In particular, for any graph G, we show a relationship between χ ′ L (G + K 1) and Δ (G). We investigate the edge-locating chromatic number of trees and present a characterization bound for any tree in terms of maximum degree, number of leaves, and the support vertices of trees. Finally, we prove that any edge-locating coloring of a graph is an edge distinguishing coloring.
Korivand et al. (Sat,) studied this question.