Strong incidence domination in some operations of fuzzy incidence graphs and application in security allocation

Abstract

This paper explores operations on fuzzy incidence graphs (FIGs), focusing on join, Cartesian product, tensor product, and composition. Emphasizing strong fuzzy incidence graphs (SFIGs), the study examines strong incidence domination (SID) and the strong incidence domination number (SIDN) in these operations. Basic properties of FIGs resulting from these operations are studied, and bounds for the SIDN of the product of two SFIGs are established for Cartesian and tensor products. The research includes FIGs with strong join and composition, as well as complete fuzzy incidence graphs (CFIGs) and FIGs with effective pairs. Additionally, the paper discusses an application of SID in security allocation.