## Innovations in Incidence Geometry

### Neighbourhood distinguishing coloring in graphs

#### Abstract

In the case of a finite dimensional vector space $V$, any ordered basis can be used to give distinct codes for elements of $V$. Chartrand et al introduced coding for vertices of a finite connected graph using distance. A binary coding of vertices of a graph (connected or disconnected) was suggested by Suganthi. Motivated by these results, a new type of coding, called neighborhood distinguishing coloring code, is introduced in this paper. A study of this code is initiated.

#### Article information

Source
Innov. Incidence Geom., Volume 13, Number 1 (2013), 135-140.

Dates
Accepted: 8 July 2012
First available in Project Euclid: 28 February 2019

https://projecteuclid.org/euclid.iig/1551323046

Digital Object Identifier
doi:10.2140/iig.2013.13.135

Zentralblatt MATH identifier
1293.05121

Subjects
Primary: 05C15: Coloring of graphs and hypergraphs

#### Citation

Ramar, Rajasekaran; Venkatasubramanian, Swaminathan. Neighbourhood distinguishing coloring in graphs. Innov. Incidence Geom. 13 (2013), no. 1, 135--140. doi:10.2140/iig.2013.13.135. https://projecteuclid.org/euclid.iig/1551323046

#### References

• G. Chartrand, L. Eroh, M. Johnson and O.R. Oellermann, Resolvability in graphs and the metric dimension of a graph, Discrete Appl. Math. 105 (2000), 99–113.
• S. Suganthi, A Study on Resolving sets in Graphs, Thesis submitted to Madurai Kamaraj University.