<p>Token Ring networks are classical interconnection structures characterized by a symmetric and cyclic topology and are widely used in distributed computing systems. In fault-resilient network design, particularly for two-fault-resilient and design-efficient models, ensuring both reliability and identifiability is essential. The mixed metric dimension, a recently introduced graph invariant, plays a significant role in this setting by enabling the unique identification of all vertices and edges through a minimal set of reference vertices. This property is especially useful for network monitoring and fault diagnosis. In this paper, we investigate the mixed metric dimension of efficient two-fault-resilient Token Ring networks. We present a structural analysis, establish theoretical bounds, and determine the exact value of the mixed metric dimension for these networks. Our results contribute to the growing interface between graph-theoretic metric parameters and the design of fault-resilient interconnection networks.</p>

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On the mixed metric dimension of efficient two-fault-resilient token Ring graphs

  • Waqar Ali

摘要

Token Ring networks are classical interconnection structures characterized by a symmetric and cyclic topology and are widely used in distributed computing systems. In fault-resilient network design, particularly for two-fault-resilient and design-efficient models, ensuring both reliability and identifiability is essential. The mixed metric dimension, a recently introduced graph invariant, plays a significant role in this setting by enabling the unique identification of all vertices and edges through a minimal set of reference vertices. This property is especially useful for network monitoring and fault diagnosis. In this paper, we investigate the mixed metric dimension of efficient two-fault-resilient Token Ring networks. We present a structural analysis, establish theoretical bounds, and determine the exact value of the mixed metric dimension for these networks. Our results contribute to the growing interface between graph-theoretic metric parameters and the design of fault-resilient interconnection networks.