Selvam Avadayappan and M. Bhuvaneshwari

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

Volume 20, 2014, Number 4, Pages 69—76

**Download full paper: PDF, 180 Kb**

## Details

### Authors and affiliations

Selvam Avadayappan

*Department of Mathematics
VHNSN College, Virudhunagar – 626001, India
*

M. Bhuvaneshwari

*Department of Mathematics
VHNSN College, Virudhunagar – 626001, India
*

### Abstract

Let *G*(*V*, *E*) be a graph. A vertex *v* ∈ *V*(*G*) is said to be a self vertex switching of *G*, if *G* is isomorphic to *G ^{v}*, where

*G*is the graph obtained from

^{v}*G*, by deleting all edges of

*G*incident to

*v*and adding edges between

*v*and the vertices which are not adjacent to

*v*in

*G*. In this paper, we discuss some applications of self vertex switching and list out all trees and unicyclic graphs with unique self vertex switching. We also obtain some more results on self vertex switching.

### Keywords

- Switching
- Self vertex switching
- Trees
- Unicyclic graphs

### AMS Classification

- 05CXX

### References

- Balakrishnan, R., K. Ranganathan, A Text Book of Graph Theory, Springer-verlag, New York, Inc, 1999.
- Jayasekaran, C., Self vertex switchings of connected graphs. Proceedings of the national conference on the emerging trends in Pure and Applied Mathematics, St. Xavier’s College, Palayamkottai, Tamilnadu, India, 2005, 154–160.
- Jayasekaran, C., On Interchange Similar Self vertex switchings of Graphs, Int. Journal of Algorithms, Computing and Mathematics, Vol. 3, February 2010, No. 1, 59–64.
- Jayasekaran, C., Graphs with a given number of self vertex switchings, Int. Journal of Algorithms, Computing and Mathematics, Vol. 3, August 2010, No. 3, 27–36.
- Seidel, J. J., A survey of two graphs, Proc. of the Inter National Coll. Theorie Comb. (Rome 1973). Tomo I, Acca, Naz. Lincei, 1976, 481–511.
- Vilfred, V., J. Paulraj Joseph, C. Jayasekaran, Branches and joints in the self vertex switchings of graphs, JCMCC Vol. 67, 2008, 111–122.

## Related papers

## Cite this paper

APAAvadayappan, S., & Bhuvaneshwari, M. (2014). Some results on self vertex switching. Notes on Number Theory and Discrete Mathematics, 20(4), 69-76.

ChicagoAvadayappan, Selvam, and M. Bhuvaneshwari. “Some Results on Self Vertex Switching.” Notes on Number Theory and Discrete Mathematics 20, no. 4 (2014): 69-76.

MLAAvadayappan, Selvam, and M. Bhuvaneshwari. “Some Results on Self Vertex Switching.” Notes on Number Theory and Discrete Mathematics 20.4 (2014): 69-76. Print.