Finding minimal Ferrers-esque graphs on path graphs ans cycle graphs via set cover

This paper presents minimal construction techniques of a new graph class called Ferrer-esque comes from Ferrers relation cite{Ferrer} on path and cycle graphs by using set cover method. The minimal constructions provide to obtain a Ferrer-esque graph by adding minimum number of edges to paths and cycles. We also state some open problems about Ferrer-Esque graphs to the readers.