Abstract
The Knödel graph \(W_{\varDelta,n}\) is a regular graph of even order and degree \(\varDelta\) where 2 \(\leq \varDelta \leq \lfloor{log_2 n}\rfloor\). Despite being a highly symmetric and widely studied graph, the diameter of \(W_{\varDelta,n}\) is known only for \(n=2^{\varDelta}\). In this paper we present a tight upper bound on the diameter of the Knödel graph for general case. We show that the presented bound differs from the diameter by at most 2 when \(\varDelta < \alpha \lfloor{\log_2 n}\rfloor\) for some 0 < α < 1 where α → 1 when n → ∞. The proof is constructive and provides a near optimal diametral path for the Knödel graph \(W_{\varDelta,n}\).
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Grigoryan, H., Harutyunyan, H.A. (2013). Tight Bound on the Diameter of the Knödel Graph. In: Lecroq, T., Mouchard, L. (eds) Combinatorial Algorithms. IWOCA 2013. Lecture Notes in Computer Science, vol 8288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45278-9_18
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DOI: https://doi.org/10.1007/978-3-642-45278-9_18
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