Abstract
Let P1 and P2 be graphical properties. A Smarandachely (P1, P2)- decomposition of a graph G is a decomposition of G into subgraphs G1,G2, � � � ,Gl ∈ P such that Gi ∈ P1 or Gi 6∈ P2 for integers 1 ≤ i ≤ l. Particularly, if P2 = ∅, i.e., a usual decomposition of a graph, is a collection of its subgraphs whose union equals the edge set of the graph. In this paper we introduce and initiate a study of a new variation of decom- position namely equiparity induced path decomposition of a graph which is defined to be a decomposition in which all the members are induced paths having same parity.
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