Nonexistence of Almost Moore Digraphs of Degrees 4 and 5 with Self-Repeats

Electronic Journal of Combinatorics

article

Nacho López¹  Arnau Messegué²  Josep M. Miret³ 

[1] Departament de Matem`atica Universitat de Lleida Lleida;Departament de Ci`encies de la Computaci´o Universitat Polit`ecnica de Catalunya Barcelona;Universitat de Lleida

DOI  :  10.37236/11335

学科分类：统计和概率

来源: Electronic Journal Of Combinatorics

【 摘 要 】

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 $k\geq 5$.

【 授权许可】

CC BY