Pseudo-Geometric Strongly Regular Graphs with a Regular Point

[2204.04755] Pseudo-Geometric Strongly Regular Graphs with a Regular Point Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Combinatorics arXiv:2204.04755 (math) [Submitted on 10 Apr 2022 ( v1 ), last revised 9 Apr 2026 (this version, v3)] Title: Pseudo-Geometric Strongly Regular Graphs with a Regular Point Authors: Edwin van Dam , Krystal Guo View a PDF of the paper titled Pseudo-Geometric Strongly Regular Graphs with a Regular Point, by Edwin van Dam and Krystal Guo View PDF HTML (experimental) Abstract: We study pseudo-geometric strongly regular graphs whose second subconstituent with respect to a vertex is a cover of a strongly regular graph or a complete graph. By studying the structure of such graphs, we characterize all graphs containing such a vertex, and use our characterization to find many new strongly regular graphs. Thereby, we answer a question posed by Gardiner, Godsil, Hensel, and Royle. We give an explicit construction for q new, pairwise non-isomorphic graphs with the same parameters as the collinearity graph of generalized quadrangles of order $(q,q)$ and a new non-geometric graph with the same parameters as the collinearity graph of the Hermitian generalized quadrangle of order $(q^2, q)$, for prime powers $q$. Using our characterization, we computed 135478 new strongly regular graphs with parameters (85,20,3,5) and 27 039 strongly regular graphs with parameters (156, 30, 4, 6). Comments: 22 pages, 4 figures Subjects: Combinatorics (math.CO) MSC classes: 05E30, 51E12, 05C50 Cite as: arXiv:2204.04755 [math.CO] (or arXiv:2204.04755v3 [math.CO] for this version) https://doi.org/10.48550/arXiv.2204.04755 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Krystal Guo [ view email ] [v1] Sun, 10 Apr 2022 19:40:47 UTC (190 KB) [v2] Thu, 16 Jun 2022 13:34:38 UTC (406 KB) [v3] Thu, 9 Apr 2026 12:18:11 UTC (191 KB) Full-text links: Access Paper: View a PDF of the paper titled Pseudo-Geometric Strongly Regular Graphs with a Regular Point, by Edwin van Dam and Krystal Guo View PDF HTML (experimental) TeX Source view license Current browse context: math.CO < prev | next > new | recent | 2022-04 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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