Maximizing spectral radius and number of spanning trees in bipartite graphs
Combinatorics
2018-09-28 v1
Abstract
The problems of maximizing the spectral radius and the number of spanning trees in a class of bipartite graphs with certain degree constraints are considered. In both the problems, the optimal graph is conjectured to be a Ferrers graph. Known results towards the resolution of the conjectures are described. We give yet another proof of a formula due to Ehrenborg and van Willigenburg for the number of spanning trees in a Ferrers graph. The main tool is a result which gives several necessary and sufficient conditions under which the removal of an edge in a graph does not affect the resistance distance between the end-vertices of another edge.
Keywords
Cite
@article{arxiv.1809.10342,
title = {Maximizing spectral radius and number of spanning trees in bipartite graphs},
author = {Ravindra Bapat},
journal= {arXiv preprint arXiv:1809.10342},
year = {2018}
}