2026-04-17T03:39:55Zhttps://recercat.cat/oai/request

oai:recercat.cat:10459.1/4657492025-09-15T18:27:28Zcom_2072_3622col_2072_479130

Almost Moore and the largest mixed graphs of diameters two and three Dalfó, Cristina Fiol Mora, Miguel Ángel López Lorenzo, Ignacio Mixed graph Degree/diameter problem Almost Moore graph Distance matrix Spectrum Almost Moore mixed 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 unit less than the Moore bound for such graphs. The problem of their existence has been considered just for diameter 2. In this paper, we give a complete characterization of these extremal mixed graphs for diameters 2 and 3. We also derive some optimal constructions for other diameters. This research has been supported by AGAUR from the Catalan Government under project 2021SGR00434 and MICINN from the Spanish Government under project PID2020-115442RB-I00. The research of M. A. Fiol was also supported by a grant from the Universitat Politècnica de Catalunya with references AGRUPS-2022 and AGRUPS-2023. 2024-07 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion https://doi.org/10.1016/j.laa.2024.01.007 0024-3795 1873-1856 https://hdl.handle.net/10459.1/465749 eng info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-115442RB-I00/ES/ Reproducció del document publicat a https://doi.org/10.1016/j.laa.2024.01.007 Linear Algebra and its Applications, 2024, vol. 693, p. 374-385. cc-by-nc-nd (c) Dalfó et al., 2024 Attribution-NonCommercial-NoDerivatives 4.0 International info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc-nd/4.0/ Elsevier