A set S of paths in ψ is said to be a Path Dominating Set (PDS) if every path not in S is ψ-adjacent to some path in S and the minimum cardinality of S is called the path domination number and it is denoted by γ_ψ (G). In this paper, some bounds for γ_ψ (G) are obtained and some properties of PDS is studied.
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