Geodesic
Nonexistence of almost Moore digraphs of diameter four
Josep Conde1 ; Joan Gimbert1 ; Josep González2 ; Josep M. Miret1 ; Ramiro Moreno1
1Universitat de Lleida
2Universitat Politècnica de Catalunya
The electronic journal of combinatorics, Tome 20 (2013) no. 1
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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 $d$.
DOI : 10.37236/2573
Classification : 05C20, 05C50, 11R18
Mots-clés : almost Moore digraph, characteristic polynomial, cyclotomic polynomial

Josep Conde  1   ; Joan Gimbert  1   ; Josep González  2   ; Josep M. Miret  1   ; Ramiro Moreno  1

1 Universitat de Lleida
2 Universitat Politècnica de Catalunya 
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     author = {Josep Conde and Joan Gimbert and Josep Gonz\'alez and Josep M. Miret and Ramiro Moreno},
     title = {Nonexistence of almost {Moore} digraphs of diameter four},
     journal = {The electronic journal of combinatorics},
     year = {2013},
     volume = {20},
     number = {1},
     doi = {10.37236/2573},
     zbl = {1266.05042},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/2573/}
}
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Josep Conde; Joan Gimbert; Josep González; Josep M. Miret; Ramiro Moreno. Nonexistence of almost Moore digraphs of diameter four. The electronic journal of combinatorics, Tome 20 (2013) no. 1. doi: 10.37236/2573

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