Work

Orthogonal signed graphs of degree 5

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.08735

Authors: Levit, Maxwell, Mohar, Bojan, Tayfeh-Rezaie, Behruz

Institutions: York University, Simon Fraser University, Institute for Research in Fundamental Sciences

Language: English

Topic: Graph theory and applications

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7212003722

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