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The unique mixed almost moore graph with parameters k = 2, r = 2 and z = 1

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Issue date
2017-11-02
Author
Buset, Dominique
López Lorenzo, Ignacio
Miret, Josep M. (Josep Maria)
Suggested citation
Buset, Dominique; López Lorenzo, Ignacio; Miret, Josep M. (Josep Maria); . (2017) . The unique mixed almost moore graph with parameters k = 2, r = 2 and z = 1. Journal of Interconnection Networks, 2017, vol. 17, núm. 3, p. 1741005-1-1741005-10. https://doi.org/10.1142/S0219265917410055.
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Abstract
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.
URI
http://hdl.handle.net/10459.1/62848
DOI
https://doi.org/10.1142/S0219265917410055
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Journal of Interconnection Networks, 2017, vol. 17, núm. 3, p. 1741005-1-1741005-10
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  • Articles publicats (Matemàtica) [266]

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  • On mixed almost Moore graphs of diameter two 

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    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 ...
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    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 ...

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