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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1393,
author = {Tom\'as Vetr\'\i k},
title = {An upper bound for graphs of diameter 3 and given degree obtained as abelian lifts of dipoles},
journal = {Discussiones Mathematicae Graph Theory},
volume = {28},
year = {2008},
pages = {91-96},
zbl = {1221.05214},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1393}
}
Tomás Vetrík. An upper bound for graphs of diameter 3 and given degree obtained as abelian lifts of dipoles. Discussiones Mathematicae Graph Theory, Tome 28 (2008) pp. 91-96. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1393/
[000] [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. | Zbl 0911.05031
[001] [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. | Zbl 1046.05023
[002] [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. | Zbl 1024.05039