Asymptotic Fibonacci cordial labeling conjecture for circulant graphs

From papers

Let Γ(n,S)\Gamma(n,S) be a circulant graph on nn vertices with connection set SS. Here, “small” means that SS is a connection set whose size is small relative to nn, although no precise threshold is specified in the source. Asymptotic Fibonacci cordial labeling conjecture. For large nn, almost every circulant graph Γ(n,S)\Gamma(n,S) with a “small” connection set SS admits a Fibonacci cordial labeling. This conjecture proposes an asymptotic abundance of Fibonacci cordial labelings for sparse or otherwise small-connection-set circulant graphs; the source provides no resolution or precise meaning of “almost every” and “small.”

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Primary source

Sarbari Mitra and Soumya Bhoumik, “A Study of Fibonacci Cordial Labeling in Structured Graph Families”, arXiv:2509.01823 (2025).

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