Diameter of General Knödel Graphs

Abstract

The Knödel graph W_Δ,n is a Δ-regular bipartite graph on n ≥ 2^Δ vertices where n is an even integer. In this paper We obtain some results about the distances of two vertices in the Knödel graphs and by them, we prove that $\text{diam}(W_{\Delta ,n})=1+\lceil \frac{n-2}{2^{\Delta }-2}\rceil$ , where Δ ≥ 2 and n ≥ (2Δ – 5)(2^Δ – 2) + 4.