Structural Properties of Zero-Divisor Hypergraph and Superhypergraph over Z_n: Girth and Helly Property.

Abstract

In this paper, we examine the structural characteristics of the Zero Divisor Hypergraph (H) and Zero Divisor Superhypergraph (SH) over the ring . We define important distinctions and similarities between these by characterizing their order, size, diameter, and girth.  The order of the Hypergraph and the Superhypergraph becomes the same

i.e. . Notably, the girth of Hypergraph is infinite, whereas the girth of Superhypergraph is  ]  if the cardinality of the vertex set is greater than 2. These results contribute to the larger study of the relationship between the Hypergraph and the Superhypergraph of .