TY - JOUR ID - 14133 TI - Total domination in cubic Knödel graphs JO - Communications in Combinatorics and Optimization JA - CCO LA - en SN - 2538-2128 AU - Jafari Rad, Nader AU - Mojdeh, Doost Ali AU - Musawi, Reza AU - Nazari, E. AD - Shahed University AD - Departtment of Mathematics, University of Mazandaran AD - Shahrood University of Technology AD - Tafresh University Y1 - 2021 PY - 2021 VL - 6 IS - 2 SP - 221 EP - 230 KW - Knodel graph KW - Domination number KW - total domination number KW - Pigeonhole Principle DO - 10.22049/cco.2020.26793.1143 N2 - A 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 $W_{3,n}$. UR - http://comb-opt.azaruniv.ac.ir/article_14133.html L1 - http://comb-opt.azaruniv.ac.ir/article_14133_065f302c60f2be489fc8794cc9dbebc0.pdf ER -