The Degree/Diameter Problem for Mixed Abelian Cayley Graphs
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This paper investigates the upper bounds for the number of vertices in mixed abelian Cayley graphs with given degree and diameter. Additionally, in the case when the undirected degree is equal to one, we give a construction that provides a lower bound.
Is part ofDiscrete Applied Mathematics, 2017, vol. 231, p. 190-197
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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.
López Lorenzo, Ignacio; Pérez Rosés, Hebert; Pujolàs Boix, Jordi; Zdimalovà, Maria (Elsevier B.V., 2016-09-27)The Degree/Diameter Problem is an extremal problem in graph theory with applications in network design. One of the main research areas in the Degree/Diameter Problem consists of finding large graphs whose order approach ...
Dalfó, Cristina; Fiol, Miguel Angel; López Lorenzo, Ignacio; Ryan, Joe (Elsevier, 2020)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 ...