Damghan University Press Journal of Holography Applications in Physics 2783-4778 6 3 2026 03 19 Integrating Fuzzy Graceful Labeling for Enhanced Prediction of Radiation Intensity in Holography 7 19 2075 10.22128/jhap.2026.3190.1177 EN J Senbagamalar Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai – 600062, India 0000-0002-1586-7622 P Devika Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai – 600062, India 0009-0002-4458-4362 Hossein Rashmanlou Canadian Quantum Research Center, 106-460 Doyle Ave, Kelowna, British Columbia V1Y 0C2, Canada Farshid Mofidnakhaei Department of Physics, Sar.C., Islamic Azad University, Sari, Iran 0000-0002-2903-0428 Journal Article 2025 12 10 The multiple classes of graphs that can be labeled gracefully are defined using the principles of neutrosophy. By imposing structural and labeling constraints on the graph, it becomes possible to define the <em>n</em>-th position uniquely under neutrosophic fuzzy conditions. The variety of vertex labels and edge labels may coincide for more than one vertex, and a complete proof of existence is provided for the neutrosophic fuzzy labeling of the graphs discussed in this research. Using the neutrosophic fuzzy framework, all three forms of uncertainty in the labeling process are effectively represented. In this work, neutrosophic fuzzy graceful labeling is further connected to applications involving UV rays generated from a point source and holography. The uncertainty-handling capability of neutrosophic fuzzy labeling allows it to model imprecise intensity variations of UV radiation and the wave-interference patterns fundamental to holographic reconstruction. Thus, we develop a systematic method for applying the neutrosophic fuzzy framework to network design, routing, and optimization problems, as well as to holographic encoding where labeling consistency and uncertainty coexist. In addition to providing representations of the proposed neutrosophic fuzzy labeling framework for selected graph families, the paper demonstrates that labeling constraints can yield consistent graph while managing uncertainty associated with complex physical inputs such as UV propagation and holographic wave patterns. Compared to classical graceful labeling, neutrosophic fuzzy labeling offers enhanced capability to incorporate and handle imprecise, fluctuating, and partially known data. This study lays the foundation for future theoretical refinement and future algorithm development for neutrosophic fuzzy graph labeling with respect to the graceful constraints relating to optical modeling, UV radiation analysis, and holographic systems.      https://jhap.du.ac.ir/article_2075_2e2c315b92a551730ef77f860e098025.pdf