scholarly journals A note on the crossing numbers of 5-regular graphs

2020 ◽  
Vol 40 (4) ◽  
pp. 1127
Author(s):  
Zhandong Ouyang
Keyword(s):  
Regular Graphs ◽  
Crossing Numbers

scholarly journals The Maximum of the Maximum Rectilinear Crossing Numbers of $d$-Regular Graphs of Order $n$

10.37236/143 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Matthew Alpert ◽  
Elie Feder ◽  
Heiko Harborth
Keyword(s):  
Complete Graph ◽  
Crossing Number ◽  
Regular Graphs ◽  
Crossing Numbers ◽  
Cycle Graph

We extend known results regarding the maximum rectilinear crossing number of the cycle graph ($C_n$) and the complete graph ($K_n$) to the class of general $d$-regular graphs $R_{n,d}$. We present the generalized star drawings of the $d$-regular graphs $S_{n,d}$ of order $n$ where $n+d\equiv 1 \pmod 2 $ and prove that they maximize the maximum rectilinear crossing numbers. A star-like drawing of $S_{n,d}$ for $n \equiv d \equiv 0 \pmod 2$ is introduced and we conjecture that this drawing maximizes the maximum rectilinear crossing numbers, too. We offer a simpler proof of two results initially proved by Furry and Kleitman as partial results in the direction of this conjecture.

scholarly journals Remarks on the energy of regular graphs

2016 ◽  
Vol 508 ◽  
pp. 133-145 ◽  
Author(s):  
V. Nikiforov
Keyword(s):  
Regular Graphs

scholarly journals The cyclic matching sequenceability of regular graphs

2021 ◽  
Author(s):  
Daniel Horsley ◽  
Adam Mammoliti
Keyword(s):  
Regular Graphs
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