A subset D of vertices of a graph G is a dominating set if for each u ∈ V (G) \ D, u is adjacent to some vertex v ∈ D. The domination number, γ(G) of G, is the minimum cardinality of a dominating set of G. A set D ⊆ V (G) is a total dominating set if for each u ∈ V (G), u is adjacent to some vertex v ∈ D. The total domination number, γt (G) of G, is the minimum cardinality of a total dominating set of G. For an even integer $nge 2$ and $1\le Delta \le lfloorlog_2nrfloor$, a Knodel graph $W_{Delta,n}$ is a $Delta$-regular bipartite graph of even order n, with vertices (i,j), for $i=1,2$ and $0le jle n/2-1$, where for every $j$, $0le jle n/2-1$, there is an edge between vertex $(1, j)$ and every vertex $(2,(j+2^k-1)$ mod (n/2)), for $k=0,1,cdots,Delta-1$. In this paper, we determine the total domination number in $3$-regular Knodel graphs $W_{3,n}$.
Jafari Rad, N., Mojdeh, D., Musawi, R., Nazari, E. (2021). Total domination in cubic Knodel graphs. Communications in Combinatorics and Optimization, 6(2), 221-230. doi: 10.22049/cco.2020.26793.1143
MLA
Nader Jafari Rad; Doost Ali Mojdeh; Reza Musawi; E. Nazari. "Total domination in cubic Knodel graphs". Communications in Combinatorics and Optimization, 6, 2, 2021, 221-230. doi: 10.22049/cco.2020.26793.1143
HARVARD
Jafari Rad, N., Mojdeh, D., Musawi, R., Nazari, E. (2021). 'Total domination in cubic Knodel graphs', Communications in Combinatorics and Optimization, 6(2), pp. 221-230. doi: 10.22049/cco.2020.26793.1143
VANCOUVER
Jafari Rad, N., Mojdeh, D., Musawi, R., Nazari, E. Total domination in cubic Knodel graphs. Communications in Combinatorics and Optimization, 2021; 6(2): 221-230. doi: 10.22049/cco.2020.26793.1143
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