Abstract:
Graphene, a single layer of carbon atoms arranged in a two- dimensionalhoneycomb lattice, has emerged as a revolutionary material due to itsexceptional electrical, thermal, and mechanical properties. These attributes havepositioned it at the forefront of research in nanoelectronics, quantum physics,and materials science. This study presents a detailed investigation into the metricdimensions of graphene, a graph-theoretical measure that captures the minimalnumber of reference points required to uniquely identify all other points in anetwork. Understanding this invariant provides insights into the topological efficiency and structural uniqueness of atomic arrangements within graphene.By modeling the atomic structure of graphene as a graph, we analyze how itsmetric dimension contributes to spatial resolution and control in nanoscalesystems. Our exploration considers how variations in lattice structure, boundaryconfigurations, and external parameters such as temperature, mechanical stress,or pressure impact the metric dimension and, consequently, the performance ofgraphene in real-world applications. We also discuss the role of symmetry andconnectivity in enhancing resolving power, which is crucial for fault detection,signal routing, and material optimization. Furthermore, this research highlightsthe broader implications of integrating mathematical graph theory with atomicscalematerials modeling. It provides a foundation for designing efficientgraphene-based devices with improved functionality and resilience. Byunveiling the intricacies of graphene’s atomic structure through the lens ofmetric dimension, this work opens new avenues for theoretical and applied innovations in nanotechnology and advanced materials engineering.
Page(s):
169-169
DOI:
DOI not available
Published:
Journal: 4th International Conference of Sciences “Revamped Scientific Outlook of 21st Century, 2025” , November 12,2025, Volume: 1, Issue: 1, Year: 2025
Keywords:
Graphene
,
Metric dimension
,
Structural Optimization
,
Nanoelectronics
,
Atomic Structure