Algorithmic Techniques for Acyclic Matching of Sustainable Well-Studied Graph Structures

Matching algorithms are fundamental tools in combinatorial problem-solving and network optimization. Acyclic matching is a variant of matching that requires cycle-free induced subgraphs. This constraint creates unique computational challenges while making it essential for applications requiring strict hierarchical structures, that prohibit feedback loops. In this paper, comprehensive algorithmic techniques for solving the acyclic matching problem for certain well-studied graph structures such as triangular, corona and friendship graphs are developed. We present efficient linear time algorithms based on the exact value of acyclic matching derived through mathematical induction. We prove that even though these classes of graphs have very different structures, they all follow the same predictable rules when it comes to acyclic matchings. This consistency allows us to design efficient algorithms that work across all these graph types. The developed algorithms not only improve the understanding of acyclic matching behavior but also support the design of efficient, cycle-free, and fault-tolerant network architectures. Such structures are essential for modern applications in communication, scheduling and molecular modeling, contributing to the creation of sustainable, intelligent and resilient systems that promote long-term connectivity and efficient resource use.