The unique mixed almost moore graph with parameters k = 2, r = 2 and z = 1
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A natural upper bound for the maximum number of vertices in a mixed graph with maximum undirected degree r, maximum directed out-degree z and diameter k is given by the mixed Moore bound. Graphs with order attaining the Moore bound are known as Moore graphs, and they are very rare. Besides, graphs with prescribed parameters and order one less than the corresponding Moore bound are known as almost Moore graphs. In this paper we prove that there is a unique mixed almost Moore graph of diameter k = 2 and parameters r = 2 and z = 1.
Is part ofJournal of Interconnection Networks, 2017, vol. 17, núm. 3, p. 1741005-1-1741005-10
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López Lorenzo, Ignacio; Miret, Josep M. (Josep Maria) (Electronic Journal of Combinatorics, 2016-04-01)Mixed almost Moore graphs appear in the context of the Degree/Diameter problem as a class of extremal mixed graphs, in the sense that their order is one less than the Moore bound for mixed graphs. The problem of their ...
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 ...
López Lorenzo, Ignacio; Pérez Rosés, Hebert (Elsevier, 2015)The Degree/diameter problem asks for the largest graphs given diameter and maximum degree. This problem has been extensively studied both for directed and undirected graphs, ando also for special classes of graphs. In this ...