Published April 21, 2015 | Version v1
Publication Open

A Construction of Small $(q-1)$-Regular Graphs of Girth 8

Creators

  • 1. University of Basilicata
  • 2. Universidad Nacional Autónoma de México
  • 3. Universitat Politècnica de Catalunya

Description

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.

⚠️ This is an automatic machine translation with an accuracy of 90-95%

Translated Description (Arabic)

في هذه الملاحظة، نقوم ببناء عائلة لانهائية جديدة من $( q -1 )$- الرسوم البيانية المنتظمة للمحيط 8 وترتيب $ 2q(q -1)^2 $ لجميع القوى الرئيسية $q\geq 16 $، وهي الأصغر المعروفة حتى الآن عندما لا يكون $ q -1 $ قوة رئيسية أو قوة أولية زائد واحد نفسه.

Translated Description (French)

Dans cette note, nous construisons une nouvelle famille infinie de graphes $( q-1)$ -réguliers de circonférence 8 et d'ordre $ 2q(q-1)^2 $ pour toutes les puissances premières $q\geq 16 $ , qui sont les plus petites connues jusqu'à présent chaque fois que $q-1 $ n' est pas une puissance première ou une puissance première plus une elle-même.

Translated Description (Spanish)

En esta nota construimos una nueva familia infinita de $(q-1)$ -gráficos regulares de circunferencia 8 y ordenamos $ 2q(q-1)^2 $ para todas las potencias principales $q\geq 16 $, que son las más pequeñas conocidas hasta ahora siempre que $q-1 $ no sea una potencia principal o una potencia principal más una en sí misma.

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Additional details

Additional titles

Translated title (Arabic)
إنشاء رسوم بيانية صغيرة (q -1 )$- منتظمة للمحيط 8
Translated title (French)
A Construction of Small $( q-1)$-Regular Graphs of Girth 8
Translated title (Spanish)
Una construcción de pequeños $(q-1)$ -Gráficos regulares de circunferencia 8

Identifiers

Other
https://openalex.org/W2157833877
DOI
10.37236/4397

Is supplement to
https://openalex.org/W3146758888 (Other)
https://openalex.org/W2949505588 (Other)
https://openalex.org/W2552197458 (Other)
https://openalex.org/W2473857262 (Other)
https://openalex.org/W2157833877 (Other)
https://openalex.org/W2012280556 (Other)
https://openalex.org/W1991809067 (Other)
https://openalex.org/W1565087095 (Other)
https://openalex.org/W1552590858 (Other)
https://openalex.org/W1484027990 (Other)

GreSIS Basics Section

Is Global South Knowledge
Yes
Country
Mexico

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