Nonexistence of Almost Moore Digraphs of Diameter Four

  • Josep Conde
  • Joan Gimbert
  • Josep González
  • Josep M. Miret
  • Ramiro Moreno
DOI: https://doi.org/10.37236/2573
Keywords: Almost Moore digraph, characteristic polynomial, cyclotomic polynomial

Abstract

Regular digraphs of degree $d>1$, diameter $k>1$ and order $N(d,k) = d+\cdots +d^k$ will be called almost Moore $(d,k)$-digraphs. So far, the problem of their existence has only been solved when $d=2, 3$ or $k = 2, 3$. In this paper we prove that almost Moore digraphs of diameter 4 do not exist for any degree $d$.

Published
2013-03-31
How to Cite
Conde, J., Gimbert, J., González, J., Miret, J. M., & Moreno, R. (2013). Nonexistence of Almost Moore Digraphs of Diameter Four. The Electronic Journal of Combinatorics, 20(1), P75. https://doi.org/10.37236/2573
Issue
Volume 20, Issue 1 (2013)
Article Number
P75