A digraph in which any two vertices have distinct degree pairs is called irregular. Sets of degree pairs for all irregular oriented graphs (also loopless digraphs and pseudodigraphs) with minimum and maximum size are determined. Moreover, a method of constructing corresponding irregular realizations of those sets is given.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1323,
author = {Zyta Dziechci\'nska-Halamoda and Zofia Majcher and Jerzy Michael and Zdzis\l aw Skupie\'n},
title = {Extremum degree sets of irregular oriented graphs and pseudodigraphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {26},
year = {2006},
pages = {317-333},
zbl = {1142.05325},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1323}
}
Zyta Dziechcińska-Halamoda; Zofia Majcher; Jerzy Michael; Zdzisław Skupień. Extremum degree sets of irregular oriented graphs and pseudodigraphs. Discussiones Mathematicae Graph Theory, Tome 26 (2006) pp. 317-333. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1323/
[000] [1] Y. Alavi, G. Chartrand, F.R.K. Chung, P. Erdös, R.L. Graham and O.R. Oel lermann, Highly irregular graphs, J. Graph Theory 11 (1987) 235-249, doi: 10.1002/jgt.3190110214. | Zbl 0665.05043
[001] [2] Y. Alavi, J. Liu and J. Wang, Highly irregular digraphs, Discrete Math. 111 (1993) 3-10, doi: 10.1016/0012-365X(93)90134-F. | Zbl 0786.05038
[002] [3] G. Chartrand and L. Lesniak, Graphs and Digraphs (Chapman and Hall, Third edition, 1996). | Zbl 0890.05001
[003] [4] Z. Dziechcińska-Halamoda, Z. Majcher, J. Michael and Z. Skupień, Large minimal irregular digraphs, Opuscula Mathematica 23 (2003) 21-24. | Zbl 1093.05505
[004] [5] M. Gargano, J.W. Kennedy and L.V. Quintas, Irregular digraphs, Congress. Numer. 72 (1990) 223-231. | Zbl 0693.05038
[005] [6] J. Górska and Z. Skupień, Near-optimal irregulation of digraphs, submitted.
[006] [7] J. Górska, Z. Skupień, Z. Majcher and J. Michael, A smallest irregular oriented graph containing a given diregular one, Discrete Math. 286 (2004) 79-88, doi: 10.1016/j.disc.2003.11.049. | Zbl 1051.05045
[007] [8] J.S. Li and K. Yang, Degree sequences of oriented graphs, J. Math. Study 35 (2002) 140-146. | Zbl 1008.05034
[008] [9] Z. Majcher and J. Michael, Degree sequences of highly irregular graphs, Discrete Math. 164 (1997) 225-236, doi: 10.1016/S0012-365X(97)84782-6. | Zbl 0870.05071
[009] [10] Z. Majcher and J. Michael, Highly irregular graphs with extreme numbers of edges, Discrete Math. 164 (1997) 237-242, doi: 10.1016/S0012-365X(96)00056-8. | Zbl 0883.05082
[010] [11] Z. Majcher and J. Michael, Degree sequences of digraphs with highly irregular property, Discuss. Math. Graph Theory 18 (1998) 49-61, doi: 10.7151/dmgt.1062. | Zbl 0915.05063
[011] [12] Z. Majcher, J. Michael, J. Górska and Z. Skupień, The minimum size of fully irregular oriented graphs, Discrete Math. 236 (2001) 263-272, doi: 10.1016/S0012-365X(00)00446-5. | Zbl 0998.05028
[012] [13] A. Selvam, Highly irregular bipartite graphs, Indian J. Pure Appl. Math. 27 (1996) 527-536. | Zbl 0853.05068
[013] [14] Z. Skupień, Problems on fully irregular digraphs, in: Z. Skupień, R. Kalinowski, guest eds., Discuss. Math. Graph Theory 19 (1999) 253-255, doi: 10.7151/dmgt.1102. | Zbl 0954.05503