On star coloring of degree splitting of join graphs

Ulagammal, S.; Vivin J., Vernold; Ulagammal, S.; Vivin J., Vernold

doi:10.22199/issn.0717-6279-2019-05-0069

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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.38 no.5 Antofagasta dic. 2019

http://dx.doi.org/10.22199/issn.0717-6279-2019-05-0069

Artículos

On star coloring of degree splitting of join graphs

S. Ulagammal¹

Vernold Vivin J.²
http://orcid.org/0000-0002-3027-2010

^¹University College of Engineering, (Anna U. Constitutent College), Nagercoil, TN, India. E-mail: ulagammal2877@gmail.com

^² University College of Engineering, (Anna U. Constitutent College), Nagercoil, TN, India. E-mail: vernoldvivin@yahoo.in

Abstract

A star coloring of a graph G is a proper vertex coloring in which every path on four vertices in G is not bicolored. The star chromatic number χ _s (G) of G is the least number of colors needed to star color G. In this paper, we have generalized the star chromatic number of degree splitting of join of any two graph G and H denoted by G + H, where G is a path graph and H is any simple graph. Also, we determine the star chromatic number for degree splitting of join of path graph G of order m with path P _n , complete graph K _n and cyclevgraph C _n .

Keywords: Star coloring; Complete graph; Path and cycle.

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References

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Received: October 30, 2018; Accepted: April 30, 2019

Article copyright: © 2019 S. Ulagammal and Vernold Vivin J. This is an open access article distributed under the terms of the Creative Commons Licence, which permits unrestricted use and distribution provided the original author and source are credited.

This is an open-access article distributed under the terms of the Creative Commons Attribution License