Mixed almost Moore graphs appear in the context of the Degree/Diameter problem as a class of extremal mixed graphs, in the sense that their order is one less than the Moore bound for mixed graphs. The problem of their existence has been considered before for directed graphs and undirected ones, but not for the mixed case, which is a kind of generalization. In this paper we give some necessary conditions for the existence of mixed almost Moore graphs of diameter two derived from the factorization in $\mathbb{Q}[x]$ of their characteristic polynomial. In this context, we deal with the irreducibility of $\Phi_i(x^2+x-(r-1))$, where $\Phi_i(x)$ denotes the i-th cyclotomic polynomial.
@article{10_37236_5647,
author = {Nacho L\'opez and Josep M. Miret},
title = {On mixed almost {Moore} graphs of diameter two},
journal = {The electronic journal of combinatorics},
year = {2016},
volume = {23},
number = {2},
doi = {10.37236/5647},
zbl = {1335.05096},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5647/}
}
TY - JOUR
AU - Nacho López
AU - Josep M. Miret
TI - On mixed almost Moore graphs of diameter two
JO - The electronic journal of combinatorics
PY - 2016
VL - 23
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/5647/
DO - 10.37236/5647
ID - 10_37236_5647
ER -
%0 Journal Article
%A Nacho López
%A Josep M. Miret
%T On mixed almost Moore graphs of diameter two
%J The electronic journal of combinatorics
%D 2016
%V 23
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/5647/
%R 10.37236/5647
%F 10_37236_5647
Nacho López; Josep M. Miret. On mixed almost Moore graphs of diameter two. The electronic journal of combinatorics, Tome 23 (2016) no. 2. doi: 10.37236/5647
