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For a simple graph G, the 3-distance graph, D₃ (G), is a graph with the vertex set V (G) and two vertices are adjacent if and only if their distance is 3 in the graph G. For a connected graph G, we provide some conditions for the connectedness of D₃ (G). Also, we characterize all trees and unicyclic graphs with connected 3-distance graph.
Musawi et al. (Sun,) studied this question.
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