scholarly journals Balloons, cut-edges, matchings, and total domination in regular graphs of odd degree

2009 ◽  
pp. n/a-n/a
Author(s):  
Suil O ◽  
Douglas B. West
Keyword(s):  
Regular Graphs ◽  
Total Domination ◽  
Odd Degree

E-Super Vertex Magic Regular Graphs of Odd Degree

2015 ◽  
Vol 48 ◽  
pp. 49-56
Author(s):  
Guang-Hui Zhang ◽  
Tao-Ming Wang
Keyword(s):  
Regular Graphs ◽  
Odd Degree

scholarly journals Even Cycles and Even 2-Factors in the Line Graph of a Simple Graph

10.37236/5660 ◽  
2017 ◽  
Vol 24 (4) ◽  
Author(s):  
Arrigo Bonisoli ◽  
Simona Bonvicini
Keyword(s):  
Perfect Matching ◽  
Line Graph ◽  
Simple Graph ◽  
Connected Components ◽  
Regular Graphs ◽  
Necessary And Sufficient Condition ◽  
Cubic Graph ◽  
Cycle Decomposition ◽  
Odd Degree ◽  
Necessary And Sufficient

Let $G$ be a connected graph with an even number of edges. We show that if the subgraph of $G$ induced by the vertices of odd degree has a perfect matching, then the line graph of $G$ has a $2$-factor whose connected components are cycles of even length (an even $2$-factor). For a cubic graph $G$, we also give a necessary and sufficient condition so that the corresponding line graph $L(G)$ has an even cycle decomposition of index $3$, i.e., the edge-set of $L(G)$ can be partitioned into three $2$-regular subgraphs whose connected components are cycles of even length. The more general problem of the existence of even cycle decompositions of index $m$ in $2d$-regular graphs is also addressed.

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 Regular Graphs of Odd Degree Are Antimagic

2014 ◽  
Vol 80 (1) ◽  
pp. 28-33 ◽  
Author(s):  
Daniel W. Cranston ◽  
Yu-Chang Liang ◽  
Xuding Zhu
Keyword(s):  
Regular Graphs ◽  
Odd Degree

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 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
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