Science in China Series A: Mathematics

, Volume 42, Issue 3, pp 264–271 | Cite as

Asymptotic enumeration theorems for the numbers of spanning trees and Eulerian trails in circulant digraphs and graphs

  • Zhang Fuji
  • Yong Xuerong


The asymptotic properties of the numbers of spanning trees and Eulerian trails in circulant digraphs and graphs are studied. Let\(C\left( {p,s_1 ,s_2 , \cdots ,s_k } \right)\) be a directed circulant graph. Let\(\left( {C\left( {p,s_1 ,s_2 , \cdots ,s_k } \right)} \right)\) and\(\left( {C\left( {p,s_1 ,s_2 , \cdots ,s_k } \right)} \right)\) be the numbers of spanning trees and of Eulerian trails, respectively. Then
$$\begin{array}{*{20}c} \begin{gathered} \lim \frac{1}{k}\sqrt[p]{{T\left( {C\left( {p,s_1 ,s_2 , \cdots ,s_k } \right)} \right)}} = 1, \hfill \\ \lim \frac{1}{{k!}}\sqrt[p]{{E\left( {C\left( {p,s_1 ,s_2 , \cdots ,s_k } \right)} \right)}} = 1, \hfill \\ \end{gathered} & {p \to \infty .} \\ \end{array} $$
Furthermore, their line digraph and iterations are dealt with and similar results are obtained for undirected circulant graphs.


asymptotic enumeration Eulerian trails graph circulant 


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Copyright information

© Science in China Press 1999

Authors and Affiliations

  • Zhang Fuji
    • 1
  • Yong Xuerong
    • 2
    • 3
  1. 1.Department of MathematicsXiamen UniversityXiamenChina
  2. 2.Department of Computer ScienceHong Kong University of Science & TechnologyHong KongChina
  3. 3.Department of MathematicsXinjiang UniversityUrumqiChina

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