Abstract
A (d,k)-digraph is a diregular digraph of degree d ≥ 4, diameter k ≥ 3 and the number of vertices d + d 2 + ... + d k. The existence problem of (d,k)-digraphs is one of difficult problem. In this paper, we will present some new necessary conditions for the existence of such digraphs.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Baskoro, E.T., Miller, M., Plesník, J.: Further results on almost Moore digraph. Ars Combinatoria 56, 43–63 (2000)
Baskoro, E.T., Miller, M., Plesník, J.: On the structure of digraphs with order close to the Moore bound. Graphs and Combinatorics 14, 109–119 (1998)
Baskoro, E.T., Miller, M., Širáň, J., dan Sutton, M.: Complete characterization of almost Moore digraphs of degree three. Journal of Graph Theory (in press)
Bermond, J.C., Delorme, C., Quisquater, J.J.: Strategies for interconnection networks: Some methods from graph theory. Journal of Parallel and Distributed Computing 3, 433–449 (1986)
Bridges, W.G., Toueg, S.: On impossibility of directed Moore graphs. J. Combinatorial Theory Series B 29, 339–341 (1980)
Fiol, M.A., Alegre, I., Yebra, J.L.A.: Line digraph iteration and the (d,k) problem for directed graphs. In: Proc. 10th Symp. Comp. Architecture, Stockholn, pp. 174–177 (1983)
Fiol, M.A., Yebra, J.L.A.: Dense bipartite digraphs. J. Graph Theory 14, 687–700 (1990)
Gimbert, J.: On the existence of (d,k)-digraphs. Discrete Mathematics 197/198, 375–391 (1999)
Gimbert, J.: Enumeration of almost Moore digraphs of diameter 2. Discrete Mathematics 231, 177–190 (2001)
Miller, M., Fris, I.: Minimum diameter of direguler digraphs of degree 2. Computer Journal 31, 71–75 (1988)
Miller, M., Fris, I.: Maximum order digraphs for diameter 2 or degree 2. In: Pullman Volume of Graphs and Matrices. Lecture Note in Pure and Applied Mathematics, vol. 139, pp. 269–298 (1992)
Miller, M., Gimbert, J., Širáň, J., Slamin: Almost Moore digraphs are diregular. Discrete Mathematics 218(1-3), 265–270 (2000)
Plesník, J., Znám, Š.: Strongly geodetic directed graphs. Acta F.R.N. Univ. Comen. Mathematica XXIX, 29–34 (1974)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cholily, Y.M., Baskoro, E.T., Uttunggadewa, S. (2005). Some Conditions for the Existence of (d,k)-Digraphs. In: Akiyama, J., Baskoro, E.T., Kano, M. (eds) Combinatorial Geometry and Graph Theory. IJCCGGT 2003. Lecture Notes in Computer Science, vol 3330. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30540-8_9
Download citation
DOI: https://doi.org/10.1007/978-3-540-30540-8_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24401-1
Online ISBN: 978-3-540-30540-8
eBook Packages: Computer ScienceComputer Science (R0)