Oriented spanning trees and stationary distribution of digraphs

By using biclique partitions of digraphs, this paper gives reduction formulas for the number of oriented spanning trees, stationary distribution vector and Kemeny's constant of digraphs. As applications, we give a method for enumerating spanning trees of undirected graphs by vertex degrees and...

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Bibliographic Details
Published inAdvances in applied mathematics Vol. 150; p. 102576
Main Authors Zhou, Jiang, Bu, Changjiang
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.09.2023
Subjects
Matrix-tree theorem
Oriented spanning tree
Random walk
Stationary distribution
05C20
Oriented spanning tree
Matrix-tree theorem
05C50
05C30
Random walk
05C81
05C05
Stationary distribution
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Summary:By using biclique partitions of digraphs, this paper gives reduction formulas for the number of oriented spanning trees, stationary distribution vector and Kemeny's constant of digraphs. As applications, we give a method for enumerating spanning trees of undirected graphs by vertex degrees and biclique partitions. The biclique partition formula also extends the results of Knuth and Levine from line digraphs to general digraphs.
ISSN:0196-8858
1090-2074
DOI:10.1016/j.aam.2023.102576