-optimal digraphs

Wang, Shiying; Lin, Shangwei

doi:10.1016/j.ipl.2008.07.008

Cited by 17 publications

(15 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As an example, consider the cycle of length k ≥ 3. In the aforementioned paper [30], Wang and Lin proved the following result.…”

Section: Terminology and Introductionmentioning

confidence: 92%

“…Theorem A. [30] Let D be a strongly connected digraph with δ + (D) ≥ 3 or δ − (D) ≥ 3. Then every element of xy is a restricted arc-cut for all xy ∈ A(D), thus, D is λ -connected.…”

Section: Terminology and Introductionmentioning

confidence: 99%

“…Some sufficient conditions for some families of digraphs to attain λ -optimality can be found in Refs. [8,14,30].…”

Section: Terminology and Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the restricted arc-connectivity of s-geodetic digraphs

Balbuena

García–Vázquez

2010

Acta. Math. Sin.-English Ser.

View full text Add to dashboard Cite

For a strongly connected digraph D the restricted arc-connectivity λ′(D) is defined as the minimum cardinality of an arc-cut over all arc-cuts S satisfying that D - S has a non-trivial strong component D₁ such that D-V (D₁) contains an arc. Let S be a subset of vertices of D. We denote by $ω^+$(S) the set of arcs uv with u ∈ S and v ∉ S, and by $ω^−$(S) the set of arcs uv with u ∉ S and v ∈ S. A digraph D = (V,A) is said to be λ′-optimal if λ′(D) = ξ′(D), where ξ′(D) is the minimum arc-degree of D defined as ξ(D) = min{ξ′(xy): xy ∈ A}, and ξ′(xy) = min{|$ω^+$({x,y})|, |$ω^−$({x,y})|, |$ω^+$(x) ∪ $ω^−$(y)|, |$ω^-$(x)∪$ω^+$(y)|}. In this paper a sufficient condition for a s-geodetic strongly connected digraph D to be λ′-optimal is given in terms of its diameter. Furthermore we see that the h-iterated line digraph $L^h$(D) of a s-geodetic digraph is λ′-optimal for certain iteration h.Postprint (published version

show abstract

“…As an example, consider the cycle of length k ≥ 3. In the aforementioned paper [30], Wang and Lin proved the following result.…”

Section: Terminology and Introductionmentioning

confidence: 92%

Section: Terminology and Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the restricted arc-connectivity of s-geodetic digraphs

Balbuena

García–Vázquez

2010

Acta. Math. Sin.-English Ser.

View full text Add to dashboard Cite

show abstract

“…The example given below shows that there exists some bipartite digraphs without minimum restricted arc-cut of the form ∂ + (X). [15].) Let D be a λ -connected digraph with λ (D) ξ (D).…”

Section: Theorem 23 Let D Be a Strongly Connected Bipartite Digraphmentioning

confidence: 99%

λ′-Optimality of Bipartite Digraphs

Chen¹,

Liu²,

Meng³

2012

Information Processing Letters

View full text Add to dashboard Cite

“…In the same paper, Volkmann proved that each strong digraph D of order n 4 and girth g = 2 or g = 3 except some families of digraphs is λ -connected and gave an upper bound of λ . In [11] the authors improved this bound and introduced the concept of λ -optimal digraphs. Furthermore, they obtained some sufficient conditions for a digraph to be λ -optimal.…”

Section: Introductionmentioning

confidence: 99%