THE REGULAR NUMBER OF A STRONGLY REGULAR FERRERS GRAPH

Abstract

In this article, we study a special kind of graph, namely Ferrers graph, which has practical applications in communication networks. The Ferrers relation was introduced for the first time [12] and has been utilized for various purposes across extensive scientific fields. The relation was employed with concept lattices in formal concept analysis [12]. Some graphs associated with the relation were again linked to concept lattices [12]. A kind of partition is presented as Ferrers diagrams. Preference modeling structures were constructed using generalized version of the relation in Social Choice Theory. In this study, we introduce a new graph class called Ferrers-esque graphs, defined by the relation. We provide a characterization of the class to determine whether an arbitrary simple graph is in the class or not – in other words, whether the graph is a Ferrers-esque graph. 'Ferrers' is used as an abbreviation for 'Ferrers-esque graph.