# Extremum degree sets of irregular oriented graphs and pseudodigraphs

Zyta Dziechcińska-Halamoda; Zofia Majcher; Jerzy Michael; Zdzisław Skupień

Discussiones Mathematicae Graph Theory (2006)

- Volume: 26, Issue: 2, page 317-333
- ISSN: 2083-5892

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topZyta Dziechcińska-Halamoda, et al. "Extremum degree sets of irregular oriented graphs and pseudodigraphs." Discussiones Mathematicae Graph Theory 26.2 (2006): 317-333. <http://eudml.org/doc/270494>.

@article{ZytaDziechcińska2006,

abstract = {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.},

author = {Zyta Dziechcińska-Halamoda, Zofia Majcher, Jerzy Michael, Zdzisław Skupień},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {irregular digraphs; degree sequences; degree sets},

language = {eng},

number = {2},

pages = {317-333},

title = {Extremum degree sets of irregular oriented graphs and pseudodigraphs},

url = {http://eudml.org/doc/270494},

volume = {26},

year = {2006},

}

TY - JOUR

AU - Zyta Dziechcińska-Halamoda

AU - Zofia Majcher

AU - Jerzy Michael

AU - Zdzisław Skupień

TI - Extremum degree sets of irregular oriented graphs and pseudodigraphs

JO - Discussiones Mathematicae Graph Theory

PY - 2006

VL - 26

IS - 2

SP - 317

EP - 333

AB - 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.

LA - eng

KW - irregular digraphs; degree sequences; degree sets

UR - http://eudml.org/doc/270494

ER -

## References

top- [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. Zbl0665.05043
- [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. Zbl0786.05038
- [3] G. Chartrand and L. Lesniak, Graphs and Digraphs (Chapman and Hall, Third edition, 1996). Zbl0890.05001
- [4] Z. Dziechcińska-Halamoda, Z. Majcher, J. Michael and Z. Skupień, Large minimal irregular digraphs, Opuscula Mathematica 23 (2003) 21-24. Zbl1093.05505
- [5] M. Gargano, J.W. Kennedy and L.V. Quintas, Irregular digraphs, Congress. Numer. 72 (1990) 223-231. Zbl0693.05038
- [6] J. Górska and Z. Skupień, Near-optimal irregulation of digraphs, submitted.
- [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. Zbl1051.05045
- [8] J.S. Li and K. Yang, Degree sequences of oriented graphs, J. Math. Study 35 (2002) 140-146. Zbl1008.05034
- [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. Zbl0870.05071
- [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. Zbl0883.05082
- [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. Zbl0915.05063
- [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. Zbl0998.05028
- [13] A. Selvam, Highly irregular bipartite graphs, Indian J. Pure Appl. Math. 27 (1996) 527-536. Zbl0853.05068
- [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. Zbl0954.05503

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