Degree diameter problem on honeycomb networks

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Issue date
2014-08-23
Author
Holub, Přemys
Miller, Mirka
Pérez Rosés, Hebert
Ryan, Joe
Suggested citation
Holub, Přemys; Miller, Mirka; Pérez Rosés, Hebert; Ryan, Joe; . (2014) . Degree diameter problem on honeycomb networks. Discrete Applied Mathematics, 2014, vol. 179, p. 139-151. https://doi.org/10.1016/j.dam.2014.07.012.
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Abstract
The degree diameter problem involves finding the largest graph (in terms of the number of vertices) subject to constraints on the degree and the diameter of the graph. Beyond the degree constraint there is no restriction on the number of edges (apart from keeping the graph simple) so the resulting graph may be thought of as being embedded in the complete graph. In a generalization of this problem, the graph is considered to be embedded in some connected host graph, in this paper the honeycomb network. We consider embedding the graph in the k-dimensional honeycomb grid and provide upper and lower bounds for the optimal graph. The particular cases of dimensions 2 and 3 are examined in detail.
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http://hdl.handle.net/10459.1/47998
DOI
https://doi.org/10.1016/j.dam.2014.07.012
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Discrete Applied Mathematics, 2014, vol. 179, p. 139-151
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