Domination in 4-regular Kn\"odel graphs

A subset $D$ of vertices of a graph $G$ is a dominating set if for each $u\in V(G)\setminus D$,$u$isadjacenttosomevertex$v\in D$. The domination number, $\gamma (G)$ of $G$, is the minimum cardinality of a dominating set of $G$. For an even integer $n\ge 2$ and $1\le \mathrm{\Delta }\le \lfloor {\log }_{2}n\rfloor$, a Kn"odel graph $W_{\mathrm{\Delta },n}$ is a $Delta$-regular bipartite graph of even order $n$, with vertices$(i,j)$, for $i=1,2$ and $0\le j\le n\mathrm{/}2-1$, where for every $j$, $0\le j\le n\mathrm{/}2-1$, there is an edge between $(1,j)$ and $(2,j+2^k-1 $\text{(mod(n/2)}$)$,for$k=0,1,\cdots,\Delta-1$. In this paper, we determine the domination number in $4$-regular Kn"odel graphs $W_{4,n}$.