Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21286220211201Total domination in cubic Knödel graphs2212301413310.22049/cco.2020.26793.1143ENNader Jafari RadShahed UniversityDoost Ali MojdehDeparttment of Mathematics, University of Mazandaran0000-0001-9373-3390Reza MusawiShahrood University of TechnologyE. NazariTafresh UniversityJournal Article20200320A subset $D$ of vertices of a graph $G$ is a dominating set if for each $u\in V(G) \setminus D$, $u$ is adjacent to some vertex $v\in D$. The domination number, $\gamma(G)$ of $G$, is the minimum cardinality of a dominating set of $G$. A set $D\subseteq V(G)$ is a total dominating set if for each $u\in V(G)$, $u$ is adjacent to some vertex $v\in D$. The total domination number, $\gamma_{t}(G)$ of $G$, is the minimum cardinality of a total dominating set of $G$. For an even integer $n\ge 2$ and $1\le \Delta \le \lfloor\log_2n\rfloor$, a Kn\"odel graph $W_{\Delta,n}$ is a $\Delta$-regular bipartite graph of even order $n$, with vertices $(i,j)$, for $i=1,2$ and $0\le j\le \frac{n}{2}-1$, where for every $j$, $0\le j\le \frac{n}{2}-1$, there is an edge between vertex $(1, j)$ and every vertex $(2,(j+2^k-1)$ mod $\frac{n}{2}$), for $k=0,1,\dots,\Delta-1$. In this paper, we determine the total domination number in $3$-regular Kn\"odel graphs $W_{3,n}$.https://comb-opt.azaruniv.ac.ir/article_14133_065f302c60f2be489fc8794cc9dbebc0.pdf