Article
| Title: | Vertex transitive graphs obtained by generalizing a left loop construction of the Hoffman-Singleton graph (English) |
| Author: | Chishwashwa, Nyumbu |
| Author: | Mwambene, Eric C. |
| Language: | English |
| Journal: | Commentationes Mathematicae Universitatis Carolinae |
| ISSN: | 0010-2628 (print) |
| ISSN: | 1213-7243 (online) |
| Volume: | 65 |
| Issue: | 2 |
| Year: | 2024 |
| Pages: | 203-213 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We construct a family of vertex transitive graphs on a left loop structure of order $2q^2$ where $q$ is a power of a prime such that $q\equiv 1 \bmod 4$. The graphs are of diameter 2. The smallest of these graphs is isomorphic to the Hoffman--Singleton graph. (English) |
| Keyword: | left loop |
| Keyword: | quasi-associative |
| Keyword: | Cayley graph |
| Keyword: | Hoffman--Singleton graph |
| Keyword: | vertex transitive |
| MSC: | 05C25 |
| MSC: | 05C60 |
| MSC: | 05C62 |
| MSC: | 05E18 |
| DOI: | 10.14712/1213-7243.2025.009 |
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| Date available: | 2025-11-12T14:41:36Z |
| Last updated: | 2025-11-14 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153169 |
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| Reference: | [3] Godsil C., Royle G.: Algebraic Graph Theory.Graduate Texts in Mathematics, 207, Springer, New York, 2001. |
| Reference: | [4] Hafner P. R.: The Hoffman–Singleton graph and its automorphisms.J. Algebraic Combin. 18 (2003), no. 1, 7–12. 10.1023/A:1025136524481 |
| Reference: | [5] Hoffman A. J., Singleton R. R.: On Moore graphs with diameters $2$ and $3$.IBM J. Res. Develop. 4 (1960), 497–504. 10.1147/rd.45.0497 |
| Reference: | [6] James L. O.: A combinatorial proof that the Moore $(7,2)$ graph is unique.Utilitas Math. 5 (1974), 79–84. |
| Reference: | [7] Mwambene E.: Characterisation of regular graphs as loop graphs.Quaest. Math. 28 (2005), no. 2, 243–250. 10.2989/16073600509486125 |
| Reference: | [8] Mwambene E.: Representing vertex-transitive graphs on groupoids.Quaest. Math. 29 (2006), no. 3, 279–284. Zbl 1107.05080, 10.2989/16073600609486163 |
| Reference: | [9] Robertson G. N.: Graphs Minimal under Girth, Valency and Connectivity Constraints.PhD Thesis, University of Waterloo, Ontario, 1969. |
| Reference: | [10] Sabidussi G.: Vertex-transitive graphs.Monatsh. Math. 68 (1964), 426–438. Zbl 0136.44608, 10.1007/BF01304186 |
| Reference: | [11] : Magma Computational Algebra System.Computational Algebra Group, School of Mathematics and Statistics, University of Sydney: http://magma.maths.usyd.edu.au . |
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