On the $p$-Schatten Energy of Bipartite Graphs

TL;DR

This paper introduces formulas for the $p$-Schatten energy of bipartite graphs and uses them to compare energies, establishing that paths have maximal $p$-Schatten energy among all trees.

Contribution

It provides new integral formulas for $p$-Schatten energy and demonstrates the maximality of paths among trees based on these formulas.

Findings

Paths have maximal $p$-Schatten energy among all trees.

New Coulson and Coulson-Jacobs formulas for $p$-Schatten energy.

Comparison of $p$-Schatten energies using a quasiorder.

Abstract

We give a Coulson integral formula and a Coulson-Jacobs formula for the $p$-Schatten energy. We use this formulas to compare the $p$-Schatten energy of different trees by using a quasiorder, and establish the maximality of paths among all trees.