A construction of dense mixed graphs of diameter 2

Title: A construction of dense mixed graphs of diameter 2
Creator: Araujo-Pardo, C.; Balbuena, C.; Miller, M.; Ždímalová, M.
Relation: Electronic Notes in Discrete Mathematics Vol. 54, p. 235-240
Publisher Link: http://dx.doi.org/10.1016/j.endm.2016.09.041
Publisher: Elsevier
Resource Type: journal article
Date: 2016
Description: A mixed graph is said to be dense, if its order is close to the Moore bound and it is optimal if there is not a mixed graph with the same parameters and bigger order. We give a construction that provides dense mixed graphs of undirected degree q, directed degree [formula could not be replicated] and order 2q² for q being an odd prime power. Since the Moore bound for a mixed graph with these parameters is equal to [formula could not be replicated] the defect of these mixed graphs is [formula could not be replicated]. In particular we obtain a known mixed Moore graph of order 18, undirected degree 3 and directed degree 1, called Bosák's graph and a new mixed graph of order 50, undirected degree 5 and directed degree 2, which is proved to be optimal.
Subject: mixed Moore graphs; projective planes
Identifier: http://hdl.handle.net/1959.13/1344987
Identifier: uon:29542
Identifier: ISSN:1571-0653
Language: eng
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