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Hamiltonian laceability in the shadow distance graph of path graphs

A connected graph G is termed hamiltonian-t-laceable (t*-laceable) if there exists in it a hamiltonian path between every pair (at least one pair) of distinct vertices u and v with the property d(u,v) = t,1≤ t ≤ diam(G), where t is a positive integer. In this paper, we establish laceability properties in the edge tolerant shadow distance graph of the path graph Pn with distance set Ds = {1,2k}.