Bounds for the L(d, 1): number of diameter 2 graphs, trees and cacti

International Journal of Mobile Network Design and Innovation

Volumn 1, Issue 2, 2006, Pages 124-135

  Kohl, Anja ^a  

^a TU BERGAKADEMIE FREIBERG   (Germany)

Author keywords

cacti; diameter 2 graphs; distance 2 labelling; L(2, 1) labelling; trees

Indexed keywords

EID: 33750115492     PISSN: 17442869     EISSN: 17442850     Source Type: Journal    
DOI: 10.1504/IJMNDI.2006.010818     Document Type: Article

References (21)

1. Bodlaender, H.L., Kloks, T., Tan, R.B. and van Leeuwen, J. (2004) ‘Approximations for λ-coloring of graphs’, Computer Journal, Vol. 47, pp.193ȓ204.
2. Calamoneri, T. and Petreschi, R. (2004) ‘L(h, 1)-labeling subclasses of planar graphs’, Journal on Parallel and Distributed Computing, Vol. 64, No. 3, pp.414ȓ426.
3. Calamoneri, T. (2004) ‘The L(h, k)-labelling problem: a survey’, Technical Report, 04/2004, Department of Computer Science University of Rome “La Sapienza”.
4. Calamoneri, T., Pelc, A. and Petreschi, R. (2004) Labeling trees with a condition at distance two, accepted to Discrete Mathematics (2004).
5. Chang, G.J. and Kuo, D. (1996) ‘The L(2, 1)-labeling on graphs’, SIAM Journal Discrete Mathematics, Vol. 9, pp.309ȓ316.
6. Chang, G.J., Ke, W., Kuo, D., Liu, D. and Yeh, R. (2000) ‘On L(d, 1)-labelings of graphs’, Discrete Mathematics, Vol. 20, pp.57ȓ66.
7. Erdös, P., Fajtlowicz, S. and Hoffman, A.J. (1980) ‘Maximum degree in graphs of diameter 2’, Networks, Vol. 10, pp.87ȓ90.
8. Fiala, J., Golovach, P.A. and Kratochvil, J. (2005) ‘Distance constrained labelings of graphs ofbounded treewidth’, Lecture, Notes in Computer Science, Vol. 3580, pp.360ȓ372.
9. Georges, J.P and Mauro, D.W. (1994) ‘On the criticality of graphs labelled with a condition at distance two’, Congressus Numerantium, Vol. 101, pp.33ȓ49.
10. Georges, J.P and Mauro, D.W. (1995) ‘Generalized vertex labelings with a condition at distance two’, Congressus Numerantium, Vol. 109, pp.141ȓ159.
11. Georges, J.P. and Mauro, D.W. (2003) ‘Labelling trees with a condition at distance two’, Discrete Mathematics, Vol. 269, pp.127ȓ148.
12. Gonçalves, D. (2005) ‘On the L(p, 1)-labelling of graphs’, DMTCS Conference Volume, AE, pp.81ȓ86.
13. Griggs, J.R. and Yeh, R.K. (1992) ‘Labelling graphs with a condition at distance 2’, SIAM Journal Discrete Mathematics, Vol. 5, No. 4, pp.586ȓ595.
14. Hale, W.K. (1980) ‘Frequency assignment: theory and applications’, Proceedings of the IEEE, Vol. 68, pp.1497ȓ1514.
15. Hoffman, J. and Singleton, R.R. (1960) ‘On moore graphs with diameters 2 and 3’, IBM Journal of Research Development, Vol. 4, pp.497ȓ504.
16. Junker, M. (2003) ‘Moore graphs, latin squares and outer autoorphisms, preprint, Albert-Ludwigs-Universität Freiburg, Germany’, Available at: http://citeseer.ist.psu.edu/694003.html.
17. Kohl, A., Schreyer, J., Tuza, Zs. and Voigt, M. (2005) ‘List version of L(d, s)-labelings’, Theoretical Computer Science, Vol. 349, No. 1, pp.92ȓ98.
18. Sakai Troxell, D. (2005) ‘On critical trees labeled with a condition at distance two’, Discrete Mathematics, Vol. 295, pp.173ȓ189.
19. Simanjuntak, R. (2003) ‘Distance-related problems in graph theory’, PhD Thesis, University of Newcastle, Australia.
20. Universitat Politécnica de Catalunya (2006) ‘The (degree, diameter) problem for graphs’, Available at: http://www.mat.upc.es/grup_de_grafs/grafs/taula_delta_d.html.
21. Wang, W-F. (2006) ‘The L(2, 1)-labelling of trees, Discrete Applied Mathematics’, Vol. 154, No. 3, pp.598ȓ603.