An improved Moore bound and some new optimal families of mixed Abelian Cayley graphs
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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.
Is part ofDiscrete Mathematics, 2020, vol. 343, núm. 10, p. 112034
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Dalfó, Cristina; Fiol, Miguel Angel; López Lorenzo, Ignacio (Elsevier B.V., 2018)A mixed graph G can contain both (undirected) edges and arcs (directed edges). Here we derive an improved Moore-like bound for the maximum number of vertices of a mixed graph with diameter at least three. Moreover, a ...
Dalfó, Cristina; Fiol, Miguel Angel; López Lorenzo, Ignacio (2020-06-06)Mixed graphs can be seen as digraphs that have both arcs and edges (or digons, that is, two opposite arcs). In this paper, we consider the case where such graphs are Cayley graphs of abelian groups. Such groups can be ...
López Lorenzo, Ignacio; Pérez Rosés, Hebert; Pujolàs Boix, Jordi (Elsevier B.V., 2016-09-26)We give an upper bound for the number of vertices in mixed abelian Cayley graphs with given degree and diameter.