Abstract Graph theory provides a comprehensive account of the interactions between objects and is widely implemented in decision-making, data analysis, and complex network modeling. In order to reflect the uncertainty, indeterminacy, and inconsistency of real-world systems, the current study uses single-valued neutrosophic fuzzy graphs ( SVNFGs ), in which every node has membership, indeterminacy, and non-membership levels. In this context, some topological numbers based on vertex degree, such as the second Zagreb number, harmonic number, and reformulated Zagreb number are examined, and the associated energy measures are also obtained. It provides an application of uncertain organizational interactions using SVNFGs , where human ratings are used to represent the degree of trust, strength of interaction, and ambiguity. Neutrosophic topological energies are proposed, and these energies are used to examine the efficiency in interactions and structural stability of the organizational network. The findings indicate that these numbers can provide significant information about group behavior, allocation of trust, and the strength of decision-making interactions during uncertainty. This paper demonstrates the feasible applicability of neutrosophic topological indicators and their efficiency to inform cognition-conscience analysis and decision-making in ambiguous and difficult organizational setups. We have taken five German companies to demonstrate the efficiency of the proposed SVNFG -based topological energy measures to determine the organizational efficiency in the uncertain and indeterminate decision environment.
Iftikhar et al. (Fri,) studied this question.