DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory  18(1) (1998)   49-61
DOI: 10.7151/dmgt.1062

DEGREE SEQUENCES OF DIGRAPHS WITH HIGHLY IRREGULAR PROPERTY

Zofia Majcher and Jerzy Michael

Institute of Mathematics, University of Opole
ul. Oleska 48, 45-052 Opole, Poland

e-mail: majcher@math.uni.opole.pl
e-mail: michael@math.uni.opole.pl

Abstract

A digraph such that for each its vertex, vertices of the out-neighbourhood have different in-degrees and vertices of the in-neighbourhood have different out-degrees, will be called an HI-digraph. In this paper, we give a characterization of sequences of pairs of out- and in-degrees of HI-digraphs.

Keywords: digraph, degree sequence, highly irregular property.

1991 Mathematics Subject Classification: 05C20.

References

[1] Y. Alavi, J. Liu, J. Wang, Highly irregular digraphs, Discrete Math. 111 (1993) 3-10, doi: 10.1016/0012-365X(93)90134-F.
[2] A.J. Hoffman, Some recent applications of the theory of linear inequalities to extremal combinatorial analysis, Proc. Symp. Appl. Math. 10 (1960) 317-327.
[3] Z. Majcher, Matrices representable by directed graphs, Archivum Mathematicum (Brno) 21 (4) (1985) 205-218.
[4] Z. Majcher, J. Michael, Degree sequences of highly irregular graphs, Discrete Math. 164 (1997) 225-236, doi: 10.1016/S0012-365X(97)84782-6.

Received 2 January 1997