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arXiv · 2311.11530

Symmetry and asymmetry between positive and negative square energies of graphs

Clive Elphick·William Linz
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Abstract

The positive and negative square energies of a graph, $s^+(G)$ and $s^-(G)$, are the sums of squares of the positive and negative eigenvalues of the adjacency matrix, respectively. The first results on square energies revealed symmetry between $s^+(G)$ and $s^-(G)$. This paper reviews examples of asymmetry between these parameters, for example using large random graphs and the ratios $s^+/s^-$ and $s^-/s^+$, as well as new examples of symmetry. We answer some questions previously asked about $s^{+}$ and $s^{-}$ and suggest several further avenues of research.

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Clive Elphick, William Linz. 2023-11-20. Symmetry and asymmetry between positive and negative square energies of graphs. https://arxiv.org/abs/2311.11530

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