Core EP, Dual Core EP and Composite Generalized Inverses for a Class of Structured Matrices

We study generalized inverses for matrices associated with double star digraphs. Explicit block formulas and existence criteria are obtained for core, dual core, core EP, and dual core EP inverses, expressed in terms of explicit algebraic criteria derived from the underlying block structure. Other combined outer pseudoinverses, combining Moore–Penrose and core-type inverses, are derived with existence criteria.