Game chromatic number of Cartesian and corona product graphs

Year 2018, Volume: 5 Issue: 3, 129 - 136, 08.10.2018

Syed Ahtsham Ul Haq Bokhary , Tanveer Iqbal Usman Ali

https://doi.org/10.13069/jacodesmath.458240

Cited By: 1

Abstract

The game chromatic number $\chi_g$ is investigated for Cartesian
product $G\square H$ and corona product $G\circ H$ of two graphs $G$
and $H$. The exact values for the game chromatic number of Cartesian
product graph of $S_{3}\square S_{n}$ is found, where $S_n$ is a
star graph of order $n+1$. This extends previous results of
Bartnicki et al. [1] and Sia [9] on the game chromatic
number of Cartesian product graphs. Let $P_m$ be the path graph on
$m$ vertices and $C_n$ be the cycle graph on $n$ vertices. We have
determined the exact values for the game chromatic number of corona
product graphs $P_{m}\circ K_{1}$ and $P_{m}\circ C_{n}$.

Keywords

Game chromatic number, Cartesian product, Corona product

References

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