A cycle of length 5 with a chordal, i.e.?an edge joining two non-adjacent vertices of the cycle, is called a graph H 5 or also an House-graph. In this paper, the spectrum of House-systems nesting C 3 -systems, C 4 -systems, C 5 -systems and together ( C 3 , C 4 , C 5 ) -systems, of all admissible indices are completely determined, without exceptions.
['Paola Bonacini', 'Mario Gionfriddo', 'Lucia Marino']
Nesting House-designs