Geodesic
A construction of small \((q-1)\)-regular graphs of girth 8
M. Abreu1 ; G. Araujo-Pardo2 ; C. Balbuena3 ; D. Labbate1
1Dipartimento di Matematica, Informatica ed Economia Università degli Studi della Basilicata Viale dell'Ateneo Lucano,10 I-85100 Potenza
2Instituto de Matemáticas Campus Juriquilla Universidad Nacional Autónoma de México Juriquilla 76230 Querétaro
3Departament de Matemática Aplicada III Universitat Politècnica de Catalunya Campus Nord, Edifici C2 C/ Jordi Girona 1-3 E-08034 Barcelona
The electronic journal of combinatorics, Tome 22 (2015) no. 2
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In this note we construct a new infinite family of $(q-1)$-regular graphs of girth 8 and order $2q(q-1)^2$ for all prime powers $q\geq 16$, which are the smallest known so far whenever $q-1$ is not a prime power or a prime power plus one itself. A corrigendum was added May 18, 2021.
DOI : 10.37236/4397
Classification : 05C69, 05C35
Mots-clés : cages, girth, Moore graphs, perfect dominating sets

M. Abreu  1   ; G. Araujo-Pardo  2   ; C. Balbuena  3   ; D. Labbate  1

1 Dipartimento di Matematica, Informatica ed Economia Università degli Studi della Basilicata Viale dell'Ateneo Lucano,10 I-85100 Potenza
2 Instituto de Matemáticas Campus Juriquilla Universidad Nacional Autónoma de México Juriquilla 76230 Querétaro
3 Departament de Matemática Aplicada III Universitat Politècnica de Catalunya Campus Nord, Edifici C2 C/ Jordi Girona 1-3 E-08034 Barcelona 
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     title = {A construction of small \((q-1)\)-regular graphs of girth 8},
     journal = {The electronic journal of combinatorics},
     year = {2015},
     volume = {22},
     number = {2},
     doi = {10.37236/4397},
     zbl = {1310.05152},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/4397/}
}
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M. Abreu; G. Araujo-Pardo; C. Balbuena; D. Labbate. A construction of small \((q-1)\)-regular graphs of girth 8. The electronic journal of combinatorics, Tome 22 (2015) no. 2. doi: 10.37236/4397

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