Soft Semigraph Isomorphisms: Classification and Characteristics

A soft set is a mathematical tool designed for managing uncertainty. Semigraph is a generalization of a graph which is different from a hypergraph. Soft semigraph was introduced by applying the concept of soft set in semigraph. Through parameterization, soft semigraph generates a series of representations of a relationship given by a semigraph. Graph isomorphism serves as a crucial method for matching patterns in a range of areas including image processing, computer and information systems, social network analysis, exploration of chemical bonds, and analysis of protein structures. In this paper, we present various kinds of isomorphisms existing among soft semigraphs, namely, [Formula: see text]-isomorphism, sev-isomorphism, se-isomorphism and sa-isomorphism. We prove that [Formula: see text]-isomorphism between soft semigraphs is also sev-isomorphism. Moreover, we establish that sev and [Formula: see text]-isomorphisms are also se-isomorphism and [Formula: see text], se and sev-isomorphisms are also sa-isomorphism. Through specific examples, we illustrate instances where the converse aspect of some of these results may not hold.