Directed Pathos Total Digraph of an Arborescence
M. C. Mahesh Kumar, H. M. Nagesh · Engineering and Applied Science Letters · 2018
For an arborescence Ar, a directed pathos total digraphis 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; uv such that u, v ∈ V (Ar) and u is adjacent to v; au (ua) such that a ∈ A(Ar) and u ∈ V (Ar) and the head (tail) of a is u; P a such that a ∈ A(Ar) and P ∈ P (Ar) and the arc a lies on the directed path P ; P i P j such that P i , P j ∈ P (Ar) and it is possible to reach the head of P j from the tail of P i through a common vertex, but it is possible to reach the head of P i from the tail of P j .For this class of digraphs we discuss the planarity; outerplanarity; maximal outerplanarity; minimally nonouterplanarity; and crossing number one properties of these digraphs.The problem of reconstructing an arborescence from its directed pathos total digraph is also presented.