Vertex Exponents of Two-Colored Extremal Ministrong Digraphs

Suwilo, Saib

doi:10.1063/1.3592472

Cited by 5 publications

(5 citation statements)

References 3 publications

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“…Let D be an asymmetric primitive two-coloured cylce of length n. If D is primitive, then n have to be odd and n ≥ 3. Furthermore, if D is asymmetric, then D has directed cycles of length 2 with composition (1, 1) T , and also has two directed cycles δ 1 and δ 2 of length n. The cycle are (5,3), (3,1) and…”

Section: Vertex Exponent Of An Asymmetric Two-coloured Cyclementioning

confidence: 99%

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Vertex Exponent of Asymmetric Two-coloured Cycle

Syahmarani

Suwilo

2020

J. of Research in Math. Trends and Tech.

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Section: Vertex Exponent Of An Asymmetric Two-coloured Cyclementioning

confidence: 99%

“…Suwilo [5] also found the vertex exponent of two-colored primitive extremal ministrong digraphs D (2) on n vertices. If D (2) has one blue arc, he showed that the exponents of vertices of D (2) lie on [n 2 − 5n + 8, n 2 − 3n + 1].…”

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confidence: 97%

Vertex Exponent of Asymmetric Two-coloured Cycle

Syahmarani

Suwilo

2020

J. of Research in Math. Trends and Tech.

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“…If the two-colored Wielandt digraph has two blue arcs then γ D (2) [9] discusses the vertex exponents of two-colored ministrong digraphs D (2) on n vertices whose underlying digraph is the primitive extremal ministrong digraph D with exp(D) = n 2 − 4n + 6.…”

Section: N the Exponent Of The Vertexmentioning

confidence: 99%

“…Lemma 3.1. [9] Let D (2) be a primitive two-colored digraph consisting of two cycles. Let v k be a vertex in D (2) and suppose there is an (s, t)-walk…”

Section: Bounds For Vertex Exponentsmentioning

confidence: 99%

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Vertex Exponents of a Class of Two-Colored Hamiltonian Digraphs

Syahmarani

Suwilo

2012

JIMS

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A two-colored digraph D (2) is primitive provided there are nonnegative integers h and k such that for each pair of not necessarily distinct vertices u and v in D (2) there exists a (h, k)-walk in D (2) from u to v. The exponent of a primitive twocolored digraph D (2) , exp(D (2)), is the smallest positive integer h + k taken over all such nonnegative integers h and k. The exponent of a vertex v in D (2) is the smallest positive integer s + t such that for each vertex u in D (2) there is an (s, t)-walk from v to u. We study the vertex exponents of primitive two-colored digraphs L (2) n on n ≥ 5 vertices whose underlying digraph is the Hamiltonian digraph consisting of the cycle v 1 → vn → v n−1 → • • • → v 2 → v 1 and the arc v 1 → v n−2. For such two-colored digraph it is known that 2n 2 − 6n + 2 ≤ exp(L (2) n) ≤ (n 3 − 2n 2 + 1)/2. We show that if exp(L (2) n) = (n 3 − 2n 2 + 1)/2, then its vertex exponents lie on [(n 3 − 2n 2 − 3n + 4)/4, (n 3 − 2n 2 + 3n + 6)/4] and if exp(L (2) n) = 2n 2 − 6n + 2, then its vertex exponents lie on [n 2 − 4n + 5, n 2 − 2n − 1].

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Local exponents of a class of two-colored digraphs consisting of two cycles with lengths 2s+1 and s

Sumardi¹,

Suwilo²

2016

AIP Conference Proceedings

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Vertex Exponents of Two-Colored Extremal Ministrong Digraphs

Cited by 5 publications

References 3 publications

Vertex Exponent of Asymmetric Two-coloured Cycle

Vertex Exponent of Asymmetric Two-coloured Cycle

Vertex Exponents of a Class of Two-Colored Hamiltonian Digraphs

Local exponents of a class of two-colored digraphs consisting of two cycles with lengths 2s+1 and s

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