We study the (D;D) and (D;N) problems for double-step digraphs considering
the unilateral distance, which is the minimum between the distance in the digraph
and the distance in its converse digraph, obtained by changing the directions
of all the arcs.
The first problem consists of maximizing the number of vertices N of a digraph,
given the maximum degree D and the unilateral diameter D , whereas the
second one consists of minimizing the unilateral diameter given the maximum
degree and the number...
We study the (D;D) and (D;N) problems for double-step digraphs considering
the unilateral distance, which is the minimum between the distance in the digraph
and the distance in its converse digraph, obtained by changing the directions
of all the arcs.
The first problem consists of maximizing the number of vertices N of a digraph,
given the maximum degree D and the unilateral diameter D , whereas the
second one consists of minimizing the unilateral diameter given the maximum
degree and the number of vertices. We solve the first problem for every value
of the unilateral diameter and the second one for some infinitely many values of
the number of vertices.
Miller and Sirán [4] wrote a comprehensive survey about (D;D) and (D;N)
problems. In particular, for the double-step graphs considering the standard
diameter, the first problem was solved by Fiol, Yebra, Alegre and Valero [3],
whereas Bermond, Iliades and Peyrat [2], and also Beivide, Herrada, Balcázar
and Arruabarrena [1] solved the (D;N) problem. In the case of the double-step
digraphs, also with the standard diameter, Morillo, Fiol and Fàbrega [5] solved
the (D;D) problem and provided some infinite families of digraphs which solve
the (D;N) problem for their corresponding numbers of vertices
Citation
Dalfo, C.; Fiol, M. The (Delta,D) and (Delta,N) problems in double-step digraphs with unilateral diameter. A: European Conference on Combinatorics, Graph Theory and Applications. "EUROCOMB 2013. European Conference on Combinatorics, Graph Theory and Applications. Pisa, Italy, September 9-13, 2013". Pisa: 2013, p. 91-96.