5 papers
Spanning tree enumeration via triangular rank-one perturbations of graph Laplacians
Christian Go, Zhong Xuan Khwa, Xinyu Luo +1
We present new short proofs of known spanning tree enumeration formulae for threshold and Ferrers graphs by showing that the Laplacian matrices of such graphs admit triangular rank…
Eigenvalues of graph Laplacians via rank-one perturbations
Steven Klee, Matthew T. Stamps
We show how the spectrum of a graph Laplacian changes with respect to a certain type of rank-one perturbation. We apply our finding to give new short proofs of the spectral version…
Linear algebraic techniques for spanning tree enumeration
Steven Klee, Matthew T. Stamps
Kirchhoff's Matrix-Tree Theorem asserts that the number of spanning trees in a finite graph can be computed from the determinant of any of its reduced Laplacian matrices. In many c…
Linear algebraic techniques for weighted spanning tree enumeration
Steven Klee, Matthew T. Stamps
The weighted spanning tree enumerator of a graph with weighted edges is the sum of the products of edge weights over all the spanning trees in . In the special case that all…
Association and Simpson conversion in contingency tables
Svante Linusson, Matthew T. Stamps
We study a generalisation of Simpson reversal (also known as Simpson's paradox or the Yule-Simpson effect) to contingency tables and characterise the cases fo…