Maximizing Spectral Radius and Number of Spanning Trees in Bipartite Graphs
Indian Statistical Institute Series
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.
Bapat, Ravindra B., "Maximizing Spectral Radius and Number of Spanning Trees in Bipartite Graphs" (2018). Book Chapters. 13.