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Author

Ya-Yang Liu

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Preprint Sep 2026

Positive and Negative Square Energies of $2$-Connected Graphs

Let $G$ be a graph of order $n$, and let $s^+(G)$ and $s^-(G)$ denote the sums of the squares of the positive and negative adjacency eigenvalues of $G$, respectively. Recently, Liu, Tang, and Zhang proved the conjecture of Elphick, Farber, Goldberg, and Wocjan that every connected graph $G$ of order $n$ satisfies $ \mi...

S. Akbari, Fu-Tao Hu, Ya-Yang Liu · 1 citation · ⚡1
Preprint Aug 2026

Extremal graphs for a conjecture on the square energy of graphs

For a graph $G$, let $s^+(G)$ and $s^-(G)$ denote the sums of the squares of its positive and negative adjacency eigenvalues. We determine all equality cases in the conjecture of Elphick, Farber, Goldberg, and Wocjan that every connected graph $G$ on $n$ vertices satisfies \[ \min \{s^+(G),s^-(G)\}\ge n-1. \] Namely, e...

Fu-Tao Hu, Ya-Yang Liu, Yi Wang · 1 citation

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