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

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2020
Author
Dalfó, Cristina
Fiol, Miguel Angel
López Lorenzo, Ignacio
Ryan, Joe
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Dalfó, Cristina; Fiol, Miguel Angel; López Lorenzo, Ignacio; Ryan, Joe; . (2020) . An improved Moore bound and some new optimal families of mixed Abelian Cayley graphs. Discrete Mathematics, 2020, vol. 343, núm. 10, p. 112034. https://doi.org/10.1016/j.disc.2020.112034.
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Abstract
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.
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http://hdl.handle.net/10459.1/69173
DOI
https://doi.org/10.1016/j.disc.2020.112034
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Discrete Mathematics, 2020, vol. 343, núm. 10, p. 112034
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cc-by-nc-nd (c) Elsevier, 2020
Except where otherwise noted, this item's license is described as cc-by-nc-nd (c) Elsevier, 2020