On mixed radial Moore graphs of diameter 3

Abstract

Radial Moore graphs and digraphs are extremal graphs related to the Moore ones where the distance-preserving spanning tree is preserved for some vertices. This leads to classify them according to their proximity to being a Moore graph or digraph. In this paper we deal with mixed radial Moore graphs, where the mixed setting allows edges and arcs as different elements. An exhaustive computer search shows the top ranked graphs for an specific set of parameters. Moreover, we study the problem of their existence by providing two infinite families for different values of the degrees and diameter 3. One of these families turns out to be optimal.

The authors would like to thank “Ministerio de Ciencia e Innovaci´on” of Spain, MCIN/AEI/10.13039/501100011033 (grant references PID2019-111536RBI00 and PID2020-115442RB-I00) and AGAUR (grants references 2017SGR1158 and 2017SGR1276). Research of J. M. Ceresuela was supported by Secretaria d’Universitats i Recerca del Departament d’Empresa i Coneixement de la Generalitat de Catalunya (grant 2020 FISDU 00596). D. Chemisana thanks “Instituci´o Catalana de Recerca i Estudis Avan¸cats (ICREA)” for the ICREA Acad`emia award.