Solution to an open problem on Laplacian ratio
Combinatorics
2024-02-27 v1
Abstract
Let G be a graph. The Laplacian ratio of G is the permanent of the Laplacian matrix of G divided by the product of degrees of all vertices. The computational complexity of Laplacian ratio is #P-complete. Brualdi and Goldwasser studied systematicly the properties of Laplacian ratios of graphs. And they proposed an open problem: what is the minimum value of the Laplacian ratios of trees with n vertices having diameter at least k ? In this paper, we give a solution to the problem.
Keywords
Cite
@article{arxiv.2402.15669,
title = {Solution to an open problem on Laplacian ratio},
author = {T. Wu},
journal= {arXiv preprint arXiv:2402.15669},
year = {2024}
}