Advancements in Soft Semigraph Isomorphisms: Unveiling Additional Characteristics

A soft set functions as a mathematical instrument crafted to handle uncertainties. Semigraph, a broader form of graph distinct from hypergraph, saw the integration of soft set principles to give rise to soft semigraph. Utilizing parameterization, soft semigraph delineates various representations of a semigraph’s relationships. The pivotal role of graph isomorphism lies in its ability to discern patterns across diverse domains such as image processing, computer systems, social network analysis, chemical bonding exploration, and protein structure analysis. Different types of isomorphisms are present within soft semigraphs, including [Formula: see text]-isomorphism, [Formula: see text]-isomorphism, [Formula: see text]-isomorphism, and [Formula: see text]-isomorphism. This paper focuses on elucidating certain characteristics associated with these isomorphisms. Additionally, we investigate the complement of a soft semigraph.