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arXiv · 2609.06778

Positive Square Energy of Graphs with Minimum Degree at Least Two

S. Akbari·Fu-Tao Hu·Ya-Yang Liu
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Abstract

Let $s^+(G)$ denote the sum of the squares of the positive adjacency eigenvalues of a graph $G$. The square-energy conjecture of Elphick, Farber, Goldberg, and Wocjan, proved by Liu, Tang, and Zhang, gives a lower bound of $n-1$ for any connected graph of order $n$. We strengthen this bound to $s^+(G)\ge n$ for every connected graph $G$ of order $n$ with minimum degree at least two, unless $G$ is a cycle.

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S. Akbari, Fu-Tao Hu, Ya-Yang Liu. 2026-09-06. Positive Square Energy of Graphs with Minimum Degree at Least Two. https://arxiv.org/abs/2609.06778

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