PreprintCC BY 4.0arXiv
Orthogonal signed graphs of degree 5
Abstract
An orthogonal signed graph is a connected signed graph whose signed adjacency matrix has pairwise orthogonal rows. They are closely related to Hadamard matrices, maximal arrangements of equiangular lines, bipartite Ramanujan graphs, and the remarkable resolution of the Sensitivity Conjecture. Orthogonal signed graphs of degree at most 4 have been completely classified, and partial results were known for degree 5. We complete the classification of orthogonal signed graphs of maximum degree 5. We also provide several new infinite families of 6- and 8-regular orthogonal signed graphs.
Related
- Degree similar and net-degree similar signed graphs
- Turán-type extremal problems for unbalanced signed graphs
- Modulo k-orientations of highly edge-connected signed graphs
- Maximum index of unbalanced signed graphs without a positive odd cycle
- Signed dual graphs and face spectral gaps of Cayley 2-complexes
BibTeX
@misc{levit2026orthogonal,
title = {{Orthogonal signed graphs of degree 5}},
author = {Maxwell Levit and Bojan Mohar and Behruz Tayfeh-Rezaie},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08735},
eprint = {2609.08735},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08735},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Orthogonal signed graphs of degree 5
AU - Maxwell Levit
AU - Bojan Mohar
AU - Behruz Tayfeh-Rezaie
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08735
UR - https://arxiv.org/abs/2609.08735
AB - An orthogonal signed graph is a connected signed graph whose signed adjacency matrix has pairwise orthogonal rows. They are closely related to Hadamard matrices, maximal arrangements of equiangular lines, bipartite Ramanujan graphs, and the remarkable resolution of the Sensitivity Conjecture. Orthogonal signed graphs of degree at most 4 have been completely classified, and partial results were known for degree 5. We complete the classification of orthogonal signed graphs of maximum degree 5. We also provide several new infinite families of 6- and 8-regular orthogonal signed graphs.
ER -