Abstract A signed hypergraph is an ordered triple S = (X, e, σ), where H = (X, e) is a hypergraph, called the underlying hypergraph of S, and σ : e → {−1, +1} is a function called the signature of S. Every signed hypergraph S = (X, E, σ) can be associated with a signing of its vertices by the function μσ , called the e-marking (or, equivalently the canonical marking) of S, defined by the rule where ex denotes the set of all edges of S that contain the vertex x. A signed hypergraph S = (X, e, σ) together with its canonical marking μσ is often denoted Sμ for convenience. Hence, given a canonically marked signed hypergraph Sμ its signed intersection graph, denoted Ω(Sμ ) has ϵ for its vertex set, edges defined by the rule and its signature ∑Ω defined by The main objective of this paper is to study in detail signed graphs that are representable as signed intersection graphs of some signed hypergraphs, or the so-called signed intersection graphs, as also study the orbit of the unary operator K that transforms ...