An Elementary Proof of a Matrix Tree Theorem for Directed Graphs

DOI10.1137/19M1265193zbMath1459.05102arXiv1904.12221OpenAlexW3047300747MaRDI QIDQ5137223

Patrick De Leenheer

Publication date: 2 December 2020

Published in: SIAM Review (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.12221

zbMATH Keywords

directed graphspanning treematrix tree theorem

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Directed graphs (digraphs), tournaments (05C20) Signed and weighted graphs (05C22)

Related Items

Planar and Toroidal Morphs Made Easier, Planar and toroidal morphs made easier, Resistance matrices of balanced directed graphs, More on minors of Hermitian (quasi-)Laplacian matrix of the second kind for mixed graphs, Matrix-tree theorem of digraphs via signless Laplacians

Cites Work

• Line-digraphs, arborescences and theorems of Tutte and Knuth
• A Combinatorial Proof of the All Minors Matrix Tree Theorem
• Algebraic Combinatorics
• Unnamed Item
• Unnamed Item