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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Miquel Àngel Fiol
Universitat Politecnica de Catalunya Barcelona, Catalonia
Electrical & Electronics Engineering

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The (Delta,D) and (Delta,N) problems in double-step digraphs with unilateral distance Cristina Dalfo; Miquel Àngel Fiol
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 2, No 1 (2014): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2014.2.1.1

Abstract

We study the (Delta,D) and (Delta,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 $\Delta$ and the unilateral diameter D*, whereas the second one (somehow dual of the first) 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 infinitely many values of the number of vertices.Moreover, we compute the mean unilateral distance of the digraphs in the families considered.
Co-Authors Cristina Dalfo