Some results on the distance spectral radius and edge-disjoint spanning trees of graphs

@misc{gao2026some,
  title = {{Some results on the distance spectral radius and edge-disjoint spanning trees of graphs}},
  author = {Yongbin Gao and Ligong Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25794},
  eprint = {2609.25794},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.25794},
}

TY  - UNPB
TI  - Some results on the distance spectral radius and edge-disjoint spanning trees of graphs
AU  - Yongbin Gao
AU  - Ligong Wang
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.25794
UR  - https://arxiv.org/abs/2609.25794
AB  - Let τ(G) denote the maximum number of edge-disjoint spanning trees in a connected graph G of order n, and let ρ_D(G) denote its distance spectral radius. For an integer k≥2, Fan, He and Zhao [Discrete Appl. Math. 376 (2025) 31--40] obtained a sharp distance spectral radius condition for τ(G)≥ k when n≥2k+6. In this paper, we fill the gap 2k≤ n≤2k+5 and thus complete the result for all n≥2k. The extremal graph given by Fan, He and Zhao remains valid for n≥2k+2, while we determine the unique extremal graph for each of the orders n=2k and n=2k+1. We further obtain sharp distance spectral radius conditions and characterize all extremal graphs under the minimum degree condition δ(G)≥ k for all n≥2k. Finally, for graphs with the stronger minimum degree condition δ(G)≥6k−4 and order n≥2δ(G)+2, we obtain a sharp distance spectral radius condition ensuring τ(G)≥ k and determine the unique extremal graph.
ER  -