Implementation of Acyclic Matching in Aerospace Technology for Honeycomb-Designed Satellite Constellations

Operational satellites are critical to modern aerospace infrastructure, supporting essential services such as communication, navigation, and global surveillance. However, the increasing density of satellites and space debris in Earth’s orbit has heightened the risk of collisions, thereby threatening network reliability. This study addresses the dual challenge of managing space debris and enhancing satellite network performance by applying the concept of acyclic matching from graph theory to satellite constellations modeled as honeycomb networks. Acyclic matching identifies edge subsets without shared nodes or cycles, enabling static signal rerouting through pre-computed, loop-free paths. This ensures fault tolerance and efficient resource allocation in increasingly complex satellite constellations. The proposed method derives the general solution for acyclic matching cardinality and determines the maximum matching set for n-dimensional honeycomb networks. This technique aligns with emerging trends in autonomous fault-tolerant systems and adaptive routing protocols, proving particularly relevant for large-scale satellite systems such as Starlink and global navigation constellations. By providing alternative communication paths in the event of satellite or link failures, the approach significantly enhances the scalability, reliability, and resilience of satellite networks, ensuring uninterrupted service and improved space traffic management in the face of rising orbital congestion.