scholarly journals Upper minus total domination in small-degree regular graphs

2007 ◽  
Vol 307 (21) ◽  
pp. 2453-2463 ◽  
Author(s):  
Hong Yan ◽  
Xiaoqi Yang ◽  
Erfang Shan
Keyword(s):  
Small Degree ◽  
Regular Graphs ◽  
Total Domination

scholarly journals Total Domination in Regular Graphs

2019 ◽  
Vol 346 ◽  
pp. 523-533
Author(s):  
Carlos Hoppen ◽  
Giovane Mansan
Keyword(s):  
Regular Graphs ◽  
Total Domination

scholarly journals Asymptotic bounds on total domination in regular graphs

2021 ◽  
Vol 344 (4) ◽  
pp. 112287
Author(s):  
Carlos Hoppen ◽  
Giovane Mansan
Keyword(s):  
Regular Graphs ◽  
Total Domination ◽  
Asymptotic Bounds

scholarly journals Total domination versus paired-domination in regular graphs

2018 ◽  
Vol 38 (2) ◽  
pp. 573 ◽  
Author(s):  
Joanna Cyman ◽  
Magda Dettlaff ◽  
Michael .A. Henning ◽  
Magdalena Lemańska ◽  
Joanna Raczek
Keyword(s):  
Regular Graphs ◽  
Total Domination ◽  
Paired Domination

Upper Bounds for k-Tuple (Total) Domination Numbers of Regular Graphs

2019 ◽  
Vol 46 (2) ◽  
pp. 573-577
Author(s):  
Sharareh Alipour ◽  
Amir Jafari ◽  
Morteza Saghafian
Keyword(s):  
Upper Bounds ◽  
Regular Graphs ◽  
Total Domination ◽  
Domination Numbers

scholarly journals One-Factorizations of Regular Graphs of Order 12

10.37236/1899 ◽  
2005 ◽  
Vol 12 (1) ◽  
Author(s):  
Petteri Kaski ◽  
Patric R. J. Östergård
Keyword(s):  
Small Degree ◽  
Regular Graphs ◽  
Steiner Triple Systems ◽  
New Approach ◽  
Triple Systems ◽  
Open Case

Algorithms for classifying one-factorizations of regular graphs are studied. The smallest open case is currently graphs of order 12; one-factorizations of $r$-regular graphs of order 12 are here classified for $r\leq 6$ and $r=10,11$. Two different approaches are used for regular graphs of small degree; these proceed one-factor by one-factor and vertex by vertex, respectively. For degree $r=11$, we have one-factorizations of $K_{12}$. These have earlier been classified, but a new approach is presented which views these as certain triple systems on $4n-1$ points and utilizes an approach developed for classifying Steiner triple systems. Some properties of the classified one-factorizations are also tabulated.

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