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

Buset, Dominique; López Lorenzo, Ignacio; Miret, Josep M. (Josep Maria)

doi:https://doi.org/10.1142/S0219265917410055

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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.

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

Is part of

Journal of Interconnection Networks, 2017, vol. 17, núm. 3, p. 1741005-1-1741005-10