Edge version of the matrix tree theorem for trees

DOI10.1080/03081080008818646zbMath0960.05067OpenAlexW2078629835MaRDI QIDQ4498328

Jerrold W. Grossman, Devadatta M. Kulkarni, Ravindra B. Bapat

Publication date: 15 August 2000

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03081080008818646

zbMATH Keywords

Laplacian matrixminorsmatrix tree theoremsystem of distinct representations

Mathematics Subject Classification ID

Trees (05C05) Determinants, permanents, traces, other special matrix functions (15A15) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50)

Related Items

Nonsingular mixed graphs with few eigenvalues greater than two ⋮ On spectral integral variations of mixed graphs ⋮ On weighted directed graphs ⋮ On edge singularity and eigenvectors of mixed graphs ⋮ Singularity of Hermitian (quasi-)Laplacian matrix of mixed graphs ⋮ Generalized matrix tree theorem for mixed graphs ⋮ The Laplacian spectrum of a mixed graph ⋮ Largest eigenvalue of a unicyclic mixed graphs ⋮ On the least eigenvalue of a unicyclic mixed graph ⋮ On eigenvectors of mixed graphs with exactly one nonsingular cycle ⋮ First eigenvalue and first eigenvectors of a nonsingular unicyclic mixed graph ⋮ Unnamed Item ⋮ The Laplacian eigenvalues of mixed graphs ⋮ First eigenvalue of nonsingular mixed graphs with given number of pendant vertices

Cites Work

• An enumerating function for spanning forests with color restrictions
• An edge version of the matrix-tree theorem and the wiener index
• Generalized matrix tree theorem for mixed graphs
• A Combinatorial Proof of the All Minors Matrix Tree Theorem
• Moore-penrose inverse of the incidence matrix of a tree
• On the adjoint of a matrix associated with trees