Directed pathos middle digraph of an arborescence
Künye
Nagesh, H. M. (2021). Directed pathos middle digraph of an arborescence. TWMS Journal of Applied and Engineering Mathematics, 11(2), 480-489.Özet
A directed pathos middle digraph of an arborescence Aᵣ, written Q = DPM(Aᵣ), is the digraph whose vertex set V (Q) = V (Aᵣ) ∪ A(Aᵣ) ∪ P(Aᵣ), where V (Aᵣ) is the vertex set, A(Aᵣ) is the arc set, and P(Aᵣ) is a directed pathos set of Aᵣ. The arc set A(Q) consists of the following arcs: ab such that a, b ∈ A(Aᵣ) and the head of a coincides with the tail of b; for every v ∈ V (Aᵣ), all arcs a1v, va2; for which v is a head of the arc a1 and tail of the arc a2 in Aᵣ; P a such that a ∈ A(Aᵣ) and P ∈ P(Aᵣ) and the arc a lies on the directed path P; PᵢiPj such that Pi, Pj ∈ P(Aᵣ) and it is possible to reach the head of Pj from the tail of Pi through a common vertex, but it is possible to reach the head of Pi from the tail of Pj . The problem of reconstructing an arborescence from its directed pathos middle digraph is presented. The characterization of digraphs whose DPM(Aᵣ) are planar; outerplanar; maximal outerplanar; and minimally non-outerplanar is studied.
Kaynak
TWMS Journal of Applied and Engineering MathematicsCilt
11Sayı
2Bağlantı
https://hdl.handle.net/11729/3125http://jaem.isikun.edu.tr/web/index.php/archive/111-vol11-no2/706
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