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 Maddede Bu Makale
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Amaç & Hipotez: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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Temel Bulgular & Veri: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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Sonuç & Katkı:We have determined the exact values for the game chromatic number of corona product graphs $P_{m}\circ K_{1}$ and $P_{m}\circ C_{n}$.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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., Ali, 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://doi.org/10.13069/jacodesmath.458240
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