Strong incidence domination index in fuzzy incidence graphs

Abstract

This article introduces the concept of the domination index in fuzzy incidence graphs (FIGs) through the use of strong incidence domination. It explores several related notions, including fuzzy incidence irredundant set, fuzzy incidence independent set, fuzzy incidence independent dominating set, upper strong incidence domination number, strong incidence irredundance number, strong incidence upper irredundance number, strong incidence independent domination number and strong incidence independence number. The article examines inequalities involving these terms and introduces the concept of the strong incidence domination degree. It defines the strong incidence domination index in FIGs based on the domination degree of vertices and discusses bounds for the index. The study extends to complete FIGs, complete bipartite FIGs, fuzzy incidence cycles (FICs), fuzzy incidence trees (FITs), and the union and join of FIGs.