Connectivity of 3-distance graphs
Abstract
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.
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