Nagesh H. M. and R. Chandrasekhar

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 21, 2015, Number 2, Pages 59—69

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## Details

### Authors and affiliations

Nagesh H. M.

*Department of Science and Humanities, PES Institute of Technology
Bangalore-560 100, India
*

R. Chandrasekhar

*Department of Mathematics, Rajiv Gandhi Institute of Technology
Bangalore-560 032, India*

### Abstract

In this paper we define the digraph valued function (digraph operator), namely the line cut vertex digraph *n*(*D*) of a digraph *D* and the directed pathos line cut vertex digraph *DPn*(*T*) of an arborescence *T*. Planarity, outer planarity, maximal outer planarity, minimally non-outer planarity, and crossing number one properties of *DPn*(*T*) are discussed. Also, the problem of reconstructing an arborescence from its directed pathos line cut vertex digraph is presented.

### Keywords

- Complete bipartite subdigraph
- Directed pathos
- Inner vertex number
- Crossing number

### AMS Classification

- 05C20

### References

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- Harary, F., & Schwenk, A. J. (1972) Evolution of the path number of a graph: Converging and packing in graphs-II, Graph Theory and Computing, Ed.Read, R.C. Academic Press,New York, 39–45.
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## Cite this paper

APANagesh H. M., & R. Chandrasekhar (2015). On directed pathos line cut vertex digraph of an arborescence. Notes on Number Theory and Discrete Mathematics, 21(2), 59-69.

ChicagoNagesh H. M., and R. Chandrasekhar. “On Directed Pathos Line Cut Vertex Digraph of an Arborescence.” Notes on Number Theory and Discrete Mathematics 21, no. 2 (2015): 59-69.

MLANagesh H. M., and R. Chandrasekhar. “On Directed Pathos Line Cut Vertex Digraph of an Arborescence.” Notes on Number Theory and Discrete Mathematics 21.2 (2015): 59-69. Print.