PDF
Discussiones Mathematicae Graph Theory 27(3) (2007)
603-610
DOI: https://doi.org/10.7151/dmgt.1386
MINIMAL NON-SELFCENTRIC RADIALLY-MAXIMAL GRAPHS OF RADIUS 4
Martin Knor
Slovak University of Technology
Faculty of Civil Engineering
Department of Mathematics, Radlinského 11
813 68 Bratislava, Slovakia
e-mail: knor@vox.svf.stuba.sk.
Abstract
There is a hypothesis that a non-selfcentric radially-maximal graph of radius r has at least 3r−1 vertices. Using some recent results we prove this hypothesis for r = 4.Keywords: non-selfcentric, radially-maximal, critical, center, radius, planar graph.
2000 Mathematics Subject Classification: 05C12.
References
[1] | F. Gliviak, M. Knor and L'. Soltés, On radially maximal graphs, Australasian J. Combin. 9 (1994) 275-284. |
[2] | A. Haviar, P. Hrnciar and G. Monoszová, Eccentric sequences and cycles in graphs, Acta Univ. M. Belii Math. 11 (2004) 7-25. |
Received 29 November 2005
Revised 14 August 2006
Accepted 10 January 2007
Close