K. Praveena, M. Venkatachalam and A. Rohini

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 25, 2019, Number 2, Pages 190—198

DOI: 10.7546/nntdm.2019.25.2.190-198

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## Details

### Authors and affiliations

K. Praveena

*Department of Computer Science,
Dr. G. R. Damodaran College of Science (Autonomous)
Coimbatore – 641 014, Tamil Nadu, India
*

M. Venkatachalam

*PG and Research Department of Mathematics,*

Kongunadu Arts and Science College (Autonomous)

Coimbatore – 641 029, Tamil Nadu, India

Kongunadu Arts and Science College (Autonomous)

Coimbatore – 641 029, Tamil Nadu, India

A. Rohini

*PG and Research Department of Mathematics,*

Kongunadu Arts and Science College (Autonomous)

Coimbatore – 641 029, Tamil Nadu, India

Kongunadu Arts and Science College (Autonomous)

Coimbatore – 641 029, Tamil Nadu, India

### Abstract

Graph coloring is one of the research areas that shaped the graph theory as we know it today. An equitable coloring of a graph *G* is a proper coloring of the vertices of *G* such that color classes differ in size by at most one. The subdivision graph *S*(*G*) of a graph *G* is the graph obtained by inserting a new vertex into every edge of *G*. Let *G*_{1} and *G*_{2} be two graphs with vertex sets *V*(*G*_{1}) and *V*(*G*_{2}), respectively. The subdivision-vertex join of two vertex disjoint graphs *G*_{1} and *G*_{2} is the graph obtained from *S*(*G*_{1}) and *G*_{2} by joining each vertex of *V*(*G*_{1}) with every vertex of *V*(*G*_{2}). In this paper, we find the equitable chromatic number of subdivision vertex join of cycle graph with path graph.

### Keywords

- Equitable coloring
- Subdivision graph
- Subdivision vertex join

### 2010 Mathematics Subject Classification

- 05C15

### References

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## Related papers

## Cite this paper

APAPraveena, K., Venkatachalam, M. (2019). Equitable coloring on subdivision vertex join of cycle *C _{m}* with path

*P*. Notes on Number Theory and Discrete Mathematics, 25(2), 190-198, doi: 10.7546/nntdm.2019.25.2.190-198.

_{n}Praveena, K., M. Venkatachalam and A. Rohini. “Equitable coloring on subdivision vertex join of cycle *C _{m}* with path

*P*.” Notes on Number Theory and Discrete Mathematics 25, no. 2 (2019): 190-198, doi: 10.7546/nntdm.2019.25.2.190-198.

_{n}Praveena, K., M. Venkatachalam and A. Rohini. “Equitable coloring on subdivision vertex join of cycle *C _{m}* with path

*P*.” Notes on Number Theory and Discrete Mathematics 25.2 (2019): 190-198. Print, doi: 10.7546/nntdm.2019.25.2.190-198.

_{n}