@article {
author = {Jafari Rad, Nader and Mojdeh, Doost Ali and Musawi, Reza and Nazari, E.},
title = {Total domination in cubic Knödel graphs},
journal = {Communications in Combinatorics and Optimization},
volume = {6},
number = {2},
pages = {221-230},
year = {2021},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2020.26793.1143},
abstract = {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 $W_{3,n}$.},
keywords = {Knodel graph,Domination number,total domination number,Pigeonhole Principle},
url = {http://comb-opt.azaruniv.ac.ir/article_14133.html},
eprint = {http://comb-opt.azaruniv.ac.ir/article_14133_065f302c60f2be489fc8794cc9dbebc0.pdf}
}