Communications of the
Korean Mathematical Society CKMS

In our study, the integration of fuzzy graphs into classical graph theory gives rise to a novel concept known as ``Fuzzy Super Subdivision." Let $SS_{f}(G)$ be the fuzzy super subdivision graphs, by substituting a complete bipartite graph $k_{(2,m)}$ $(m=1,2,\ldots)$ for each edge of a fuzzy graph. The attributes and properties of this newly proposed concept are briefly outlined, in addition to illustrative examples. Furthermore, significant findings are discussed on connectivity, size, degree and order of fuzzy super subdivision structures. To illustrate the practical implications of our approach, we present an application focused on analyzing the growth of infections in blood or urine samples using the Fuzzy Super Subdivision model.

Keywords: Subdivision, super subdivision, fuzzy graphs, complete bipartite, size of super subdivision

MSC numbers: 05C72, 03B52, 94D05