Roman domination parameters with respect to differentials in probabilistic neural networks
International Journal of Wavelets, Multiresolution and Information Processing, vol.24, no.4, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 24 Issue: 4
- Publication Date: 2026
- Doi Number: 10.1142/s0219691326500190
- Journal Name: International Journal of Wavelets, Multiresolution and Information Processing
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Applied Science & Technology Source, Compendex, MathSciNet, zbMATH, Academic Search Ultimate (EBSCO), Engineering Source (EBSCO), Technology Collection (ProQuest)
- Keywords: Differential, probabilistic neural networks, Roman domination
- Dokuz Eylül University Affiliated: Yes
Abstract
The differential theory of graphs is perfectly integrated into domination theory, providing a robust framework for investigating Roman domination parameters without relying on functions. By applying proven Gallai-type theorems that link differentials and Roman domination parameters, this study highlights the practical advantages of computing either parameter. Specifically, this paper focuses on computing the differential, 2-packing differential, perfect differential and restrained differential of three- and four-layered Probabilistic Neural Networks (PNNs). Given that evaluating such network invariants is critical to understanding structural dynamics, we address relevant NP-complete problems by analyzing the topological graph configurations of these PNNs. Furthermore, a comprehensive structural characterization of the dominant differential and Roman graph classes within these network architectures is provided.