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On singular values and trace norm of signed digraphs

  • Mushtaq A. Bhat
  • Peer Abdul Manan
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Abstract

Let S = (D, Οƒ) be a signed digraph, where D=(𝒱,π’œ) is the underlying digraph of S and Οƒ:π’œβ†’{βˆ’1,+1} is a sign function. In this paper, we study the adjacency singular values of signed digraphs. We provide a necessary and sufficient condition for the singular values of a digraph to remain invariant under signing. We study rank of signed digraphs and determine signed digraphs with rank one. As an application of this result, we obtain a lower bound for the trace norm of signed digraphs and characterize the extremal signed digraphs.

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Cite

BibTeXRIS
BibTeX
@misc{bhat2026singular,
  title = {{On singular values and trace norm of signed digraphs}},
  author = {Mushtaq A. Bhat and Peer Abdul Manan},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.15829},
  eprint = {2606.15829},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.15829},
}
RIS
TY  - UNPB
TI  - On singular values and trace norm of signed digraphs
AU  - Mushtaq A. Bhat
AU  - Peer Abdul Manan
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2606.15829
UR  - https://arxiv.org/abs/2606.15829
AB  - Let S = (D, Οƒ) be a signed digraph, where D=(𝒱,π’œ) is the underlying digraph of S and Οƒ:π’œβ†’{βˆ’1,+1} is a sign function. In this paper, we study the adjacency singular values of signed digraphs. We provide a necessary and sufficient condition for the singular values of a digraph to remain invariant under signing. We study rank of signed digraphs and determine signed digraphs with rank one. As an application of this result, we obtain a lower bound for the trace norm of signed digraphs and characterize the extremal signed digraphs.
ER  -