An improved Moore bound and some new optimal families of mixed Abelian Cayley graphs

Title: An improved Moore bound and some new optimal families of mixed Abelian Cayley graphs
Creator: Dalfó, James C.; Fiol, M. A.; López, N.; Ryan, J.
Relation: Discrete Mathematics Vol. 343, Issue 10, no. 112034
Publisher Link: http://dx.doi.org/10.1016/j.disc.2020.112034
Publisher: Elsevier
Resource Type: journal article
Date: 2020
Description: We consider the case in which mixed graphs (with both directed and undirected edges) are Cayley graphs of Abelian groups. In this case, some Moore bounds were derived for the maximum number of vertices that such graphs can attain. We first show these bounds can be improved if we know more details about the order of some elements of the generating set. Based on these improvements, we present some new families of mixed graphs. For every fixed value of the degree, these families have an asymptotically large number of vertices as the diameter increases. In some cases, the results obtained are shown to be optimal.
Subject: mixed graph; degree/diameter problem; Moore bound; Cayley graph; Abelian group; congruences in Zn
Identifier: http://hdl.handle.net/1959.13/1426943
Identifier: uon:38494
Identifier: ISSN:0012-365X
Language: eng
Reviewed

		Thumbnail	File	Description	Size	Format