The minimum size of fully irregular oriented graphs

Majcher, Zofia; Michael, Jerzy; Górska, Joanna

doi:10.1016/s0012-365x(00)00446-5

Cited by 4 publications

(8 citation statements)

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“…For more information on t and m see [4,5]. In the paper [1] parameters t and m have used to the characterization of the family of all degree sets of smallest irregular oriented graphs with given order n. In particular, n-element sets (n > 3) of the following form (2):…”

Section: Propertymentioning

confidence: 99%

“…The class of digraphs with this property of irregularity was introduced in the paper [3]. Properties of oriented graphs (digraphs) of above class were studied in papers [1,2,3,4] and [5]. In particular, the minimum and the maximum size of these graphs have been found in papers [1] and [5].…”

Section: Introductionmentioning

confidence: 99%

“…In similar way we define a largest and a smallest digraph. The results of papers [1,3] and [5] permit to obtain in simple way the following properties.…”

mentioning

confidence: 99%

“…and L 5 , R 5 be sequences described in (3), (4), (5) and (6), respectively, for p = t, q = m and z j = b s t−1 +j , j = 1, 2, . .…”

mentioning

confidence: 99%

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

Dziechcińska-Halamoda

Majcher

Michael

2007

Discuss. Math. Graph Theory

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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 612 Z. Dziechcińska-Halamoda, Z. Majcher, ... 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 digraphs) of all intermediate sizes.

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Section: Propertymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Dziechcińska-Halamoda

Majcher

Michael

2007

Discuss. Math. Graph Theory

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“…The degree pair of a vertex is the outdegree followed by the indegree of the vertex. The notion of fully irregular digraphs-introduced by the present author in 1995-is investigated in [1,2,3,5]. Some results on fully irregular digraphs were presented at international conferences held in Poland at Lubiatów '96, Gronów '97, '98, and at Kazimierz Dolny '97.…”

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confidence: 99%