Kn\"odel graph

Kn\"{o}del graph -- граф Кнёделя.

The Kn\"{odel graph} on [math]\displaystyle{ n \geq 2 }[/math] vertices ([math]\displaystyle{ n }[/math] even) and of maximum degree [math]\displaystyle{ \Delta \geq 1 }[/math] is denoted [math]\displaystyle{ W_{\Delta,n} }[/math]. The vertices of [math]\displaystyle{ W_{\Delta,n} }[/math] are the couples [math]\displaystyle{ (i,j) }[/math] with [math]\displaystyle{ i = 1,2 }[/math] and [math]\displaystyle{ 0 \leq j \leq \frac{n}{2} - 1 }[/math]. For every [math]\displaystyle{ j }[/math], [math]\displaystyle{ 0 \leq j \leq \frac{n}{2} - 1 }[/math], there is an edge between vertex [math]\displaystyle{ (1,j) }[/math] and every vertex [math]\displaystyle{ (2,j+2^{k} - 1\pmod{\frac{n}{2}} }[/math], for [math]\displaystyle{ k = 0, \ldots, \Delta - 1 }[/math].