| Summary: | Consider an undirected and connected graph <inline-formula> <math display="inline"> <semantics> <mrow> <mi>G</mi> <mo>=</mo> <mo>(</mo> <msub> <mi>V</mi> <mi>G</mi> </msub> <mo>,</mo> <msub> <mi>E</mi> <mi>G</mi> </msub> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>, where <inline-formula> <math display="inline"> <semantics> <msub> <mi>V</mi> <mi>G</mi> </msub> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <msub> <mi>E</mi> <mi>G</mi> </msub> </semantics> </math> </inline-formula> represent the set of vertices and the set of edges respectively. The concept of edge version of metric dimension and doubly resolving sets is based on the distances of edges in a graph. In this paper, we find the edge version of metric dimension and doubly resolving sets for the necklace graph.
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