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arXiv · 1809.10342

Maximizing spectral radius and number of spanning trees in bipartite graphs

Ravindra Bapat
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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.

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Ravindra Bapat. 2018-09-27. Maximizing spectral radius and number of spanning trees in bipartite graphs. https://arxiv.org/abs/1809.10342

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