Geodesic
Nonexistence of almost Moore digraphs of degrees 4 and 5 with self-repeats
Nacho López ; Arnau Messegué ; Josep M. Miret1
1Universitat de Lleida
The electronic journal of combinatorics, Tome 30 (2023) no. 1
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

An almost Moore $(d,k)$-digraph is a regular digraph of degree $d>1$, diameter $k>1$ and order $N(d,k)=d+d^2+\cdots +d^k$. So far, their existence has only been shown for $k=2$, whilst it is known that there are no such digraphs for $k=3$, $4$ and for $d=2$, $3$ when $k\geq 3$. Furthermore, under certain assumptions, the nonexistence for the remaining cases has also been shown. In this paper, we prove that $(4,k)$ and $(5,k)$-almost Moore digraphs with self-repeats do not exist for $k\geq 5$.
DOI : 10.37236/11335
Classification : 05C20, 05C35, 05C50
Mots-clés : almost Moore \((d, k)\)-digraphs, permutation cycle structures

Nacho López    ; Arnau Messegué    ; Josep M. Miret  1

1 Universitat de Lleida 
@article{10_37236_11335,
     author = {Nacho  L\'opez and Arnau  Messegu\'e and Josep M. Miret},
     title = {Nonexistence of almost {Moore} digraphs of degrees 4 and 5 with self-repeats},
     journal = {The electronic journal of combinatorics},
     year = {2023},
     volume = {30},
     number = {1},
     doi = {10.37236/11335},
     zbl = {1511.05086},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/11335/}
}
TY  - JOUR
AU  - Nacho  López
AU  - Arnau  Messegué
AU  - Josep M. Miret
TI  - Nonexistence of almost Moore digraphs of degrees 4 and 5 with self-repeats
JO  - The electronic journal of combinatorics
PY  - 2023
VL  - 30
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.37236/11335/
DO  - 10.37236/11335
ID  - 10_37236_11335
ER  - 
%0 Journal Article
%A Nacho  López
%A Arnau  Messegué
%A Josep M. Miret
%T Nonexistence of almost Moore digraphs of degrees 4 and 5 with self-repeats
%J The electronic journal of combinatorics
%D 2023
%V 30
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/11335/
%R 10.37236/11335
%F 10_37236_11335
Nacho  López; Arnau  Messegué; Josep M. Miret. Nonexistence of almost Moore digraphs of degrees 4 and 5 with self-repeats. The electronic journal of combinatorics, Tome 30 (2023) no. 1. doi: 10.37236/11335

Cité par Sources :