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Degree sequences of digraphs with highly irregular property

Zofia MajcherJerzy Michael — 1998

Discussiones Mathematicae Graph Theory

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.

A Sokoban-type game and arc deletion within irregular digraphs of all sizes

Zyta Dziechcińska-HalamodaZofia MajcherJerzy MichaelZdzisław Skupień — 2007

Discussiones Mathematicae Graph Theory

Digraphs in which ordered pairs of out- and in-degrees of vertices are mutually distinct are called irregular, see Gargano et al. [3]. Our investigations focus on the problem: what are possible sizes of irregular digraphs (oriented graphs) for a given order n? We show that those sizes in both cases make up integer intervals. The extremal sizes (the endpoints of these intervals) are found in [1,5]. In this paper we construct, with help of Sokoban-type game, n-vertex irregular oriented graphs (irregular...

Extremum degree sets of irregular oriented graphs and pseudodigraphs

Zyta Dziechcińska-HalamodaZofia MajcherJerzy MichaelZdzisław Skupień — 2006

Discussiones Mathematicae Graph Theory

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.

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