Discussiones Mathematicae Graph Theory 28(1) (2008) 91-96
doi: 10.7151/dmgt.1393

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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