PreprintCC0arXiv
Positive Square Energy of Graphs with Minimum Degree at Least Two
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)≥ n for every connected graph G of order n with minimum degree at least two, unless G is a cycle.
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BibTeX
@misc{akbari2026positive,
title = {{Positive Square Energy of Graphs with Minimum Degree at Least Two}},
author = {S. Akbari and Fu-Tao Hu and Ya-Yang Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06778},
eprint = {2609.06778},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06778},
note = {CC0},
}
RIS
TY - UNPB
TI - Positive Square Energy of Graphs with Minimum Degree at Least Two
AU - S. Akbari
AU - Fu-Tao Hu
AU - Ya-Yang Liu
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2609.06778
UR - https://arxiv.org/abs/2609.06778
AB - 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)≥ n for every connected graph G of order n with minimum degree at least two, unless G is a cycle.
ER -