On directed pathos line cut vertex digraph of an arborescence

Nagesh H. M. and R. Chandrasekhar
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 21, 2015, Number 2, Pages 59–69
Full paper (PDF, 630 Kb)

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

1. Aigner, M. (1967) On the line graph of a directed graph, Math. Zeitschr, 102, 56–61.
2. Chandrasekhar, R. (2004) Some Topics in Graph Theory, Doctoral Thesis, Bangalore University, Karnataka State, India.
3. Harary, F. (1969) Graph Theory, Addison-Wesley, Reading, Mass.
4. Harary, F. (1970) Covering and packing in graphs-I, Annals of New York Academy of Science, 175, 198–205.
5. 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.
6. Bang-Jensen, J., & Gutin, G. (2009) Digraphs Theory, Algorithms and Applications,Springer.
7. Kulli, V. R. (1975) On minimally non-outer planar graphs, Proc. Indian Nat. Sci. Acad., 41,276–280.
8. Stanton, R. G., Cowan, D. D., & James, L. O. (1970) Some results on path numbers, Proceedings of the Louisiana Conference on Combinatorics, Graph Theory and Computing,112–135.