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Discussiones Mathematicae Graph Theory 28(1) (2008)
91-96
DOI: https://doi.org/10.7151/dmgt.1393
AN UPPER BOUND FOR GRAPHS OF DIAMETER 3 AND GIVEN DEGREE OBTAINED AS ABELIAN LIFTS OF DIPOLES
Tomás Vetrík
Department of Mathematics, SvF
Slovak University of Technology
Bratislava, Slovakia
e-mail: vetrik@math.sk
Abstract
We derive an upper bound on the number of vertices in graphs of diameter 3 and given degree arising from Abelian lifts of dipoles with loops and multiple edges.Keywords: degree and diameter of a graph, dipole.
2000 Mathematics Subject Classification: 05C12, 05C35.
References
[1] | B.D. McKay, M. Miller and J. Sirán, A note on large graphs of diameter two and given maximum degree, J. Combin. Theory (B) 74 (1998) 110-118, doi: 10.1006/jctb.1998.1828. |
[2] | J. Siagiová, A Moore-like bound for graphs of diameter 2 and given degree, obtained as Abelian lifts of dipoles, Acta Math. Univ. Comenianae 71 (2002) 157-161. |
[3] | J. Siagiová, A note on the McKay-Miller-Sirán graphs, J. Combin. Theory (B) 81 (2001) 205-208, doi: 10.1006/jctb.2000.2006. |
Received 29 September 2006
Revised 13 February 2007
Accepted 13 February 2007
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