Nesting House-designs

A cycle of length 5 with a chordal  , i.e. an edge joining two non-adjacent vertices of the cycle, is called a graph H5H5 or also an House-graph  . In this paper, the spectrum of House-systems nesting C3C3-systems, C4C4-systems, C5C5-systems and together (C3,C4,C5)(C3,C4,C5)-systems, of all admissible indices are completely determined, without exceptions.