We have determined the exact values for the game chromatic number of corona product graphs $P_{m}\circ K_{1}$ and $P_{m}\circ C_{n}$.
📌 3 Key Takeaways
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Objective & Hypothesis: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 $H$.
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Key Findings & Data: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 $n+1$.
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Conclusion & Impact:We have determined the exact values for the game chromatic number of corona product graphs $P_{m}\circ K_{1}$ and $P_{m}\circ C_{n}$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Game chromatic number · Cartesian product · Corona product
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 $P_{m}\circ C_{n}$.
BOKHARY, S. A. U. H., IQBAL, T., ALİ, U. (2018). Game chromatic number of Cartesian and corona product graphs. Journal of Algebra Combinatorics Discrete Structures and Applications, Cilt: 5 - Sayı: 3, 129–136. https://ajindex.com/articles/861543
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