Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Akbari, S., Hu, Fu-Tao, Liu, Ya-Yang
Institutions: Sharif University of Technology, Anhui University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G478768364
OpenAlex ID: W7211986434