Asymptotic Enumeration ofk-Edge-Coloredk-Regular Graphs

2010 ◽  
Vol 23 (4) ◽  
pp. 2178-2197
Author(s):  
Jeanette C. McLeod
Keyword(s):  
Regular Graphs ◽  
Asymptotic Enumeration

scholarly journals Exchangeable Pairs, Switchings, and Random Regular Graphs

10.37236/4659 ◽  
2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Tobias Johnson
Keyword(s):  
Spectral Properties ◽  
Regular Graphs ◽  
Asymptotic Enumeration ◽  
Linear Eigenvalue Statistics ◽  
Exchangeable Pairs ◽  
Interesting Connection ◽  
Random Regular Graph ◽  
Eigenvalue Statistics ◽  
Combinatorial Technique ◽  
Variation Distance

We consider the distribution of cycle counts in a random regular graph, which is closely linked to the graph's spectral properties. We broaden the asymptotic regime in which the cycle counts are known to be approximately Poisson, and we give an explicit bound in total variation distance for the approximation. Using this result, we calculate limiting distributions of linear eigenvalue statistics for random regular graphs. Previous results on the distribution of cycle counts by McKay, Wormald, and Wysocka (2004) used the method of switchings, a combinatorial technique for asymptotic enumeration. Our proof uses Stein's method of exchangeable pairs and demonstrates an interesting connection between the two techniques.

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

Regular graphs of girth 5 from elliptic semiplanes of type C

2021 ◽  
Vol 344 (6) ◽  
pp. 112343
Author(s):  
E. Abajo ◽  
M. Bendala
Keyword(s):  
Regular Graphs ◽  
Type C
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