Asymptotic enumeration theorems for the numbers of spanning trees and Eulerian trails in circulant digraphs and graphs
The authors established asymptotic formulas for the number of spanning trees and the number of Eulerian trails in circulant digraphs and in circulant graphs. In particular, if \(T\) is the number of spanning trees and \(E\) is the number of Eulerian trails in any circulant digraph with \(p\) vertices and out-degree \(k\) then it is shown that \({1\over k}[T]^{{1\over p}}\sim 1\) and \({1\over k!}[E]^{{1\over p}}\sim 1\) for \(p\to\infty\). Additional results are established for line graphs and for circulant graphs.
scientific article; zbMATH DE number 1329996
scientific article