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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

Abstract

References

  • [1] T. Bartnicki, B. Brešar, J. Grytczuk, M. Kovše, Z. Miechowicz, I. Peterin, Game chromatic number of Cartesian product graphs, Electron. J. Combin. 15 (2008) R72.
  • [2] H. L. Bodlaender, On the complexity of some coloring games, Int. J. Found. Comput. Sci. 2(2) (1991) 133–147.
  • [3] U. Faigle, U. Kern, H. Kierstead, W. T. Trotter, On the game chromatic number of some classes of graphs, Ars Combin. 35 (1993) 143–150.
  • [4] H. A. Kierstead, W. T. Trotter, Planar graph coloring with uncooperative partner, J. Graph Theory 18(6) (1994) 569–584.
  • [5] C. Sia, The game chromatic number of some families of Cartesian product graphs, AKCE Int. J. Graphs Comb. 6(2) (2009) 315–327.
  • [6] X. Zhu, Game coloring the Cartesian product of graphs, J. Graph Theory 59(4) (2008) 261–278.

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

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

  • [1] T. Bartnicki, B. Brešar, J. Grytczuk, M. Kovše, Z. Miechowicz, I. Peterin, Game chromatic number of Cartesian product graphs, Electron. J. Combin. 15 (2008) R72.
  • [2] H. L. Bodlaender, On the complexity of some coloring games, Int. J. Found. Comput. Sci. 2(2) (1991) 133–147.
  • [3] U. Faigle, U. Kern, H. Kierstead, W. T. Trotter, On the game chromatic number of some classes of graphs, Ars Combin. 35 (1993) 143–150.
  • [4] H. A. Kierstead, W. T. Trotter, Planar graph coloring with uncooperative partner, J. Graph Theory 18(6) (1994) 569–584.
  • [5] C. Sia, The game chromatic number of some families of Cartesian product graphs, AKCE Int. J. Graphs Comb. 6(2) (2009) 315–327.
  • [6] X. Zhu, Game coloring the Cartesian product of graphs, J. Graph Theory 59(4) (2008) 261–278.
There are 6 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Syed Ahtsham Ul Haq Bokhary

Tanveer Iqbal This is me

Usman Ali This is me

Publication Date October 8, 2018
Published in Issue Year 2018 Volume: 5 Issue: 3

Cite

APA 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, 5(3), 129-136. https://doi.org/10.13069/jacodesmath.458240
AMA Bokhary SAUH, Iqbal T, Ali U. Game chromatic number of Cartesian and corona product graphs. Journal of Algebra Combinatorics Discrete Structures and Applications. October 2018;5(3):129-136. doi:10.13069/jacodesmath.458240
Chicago Bokhary, Syed Ahtsham Ul Haq, Tanveer Iqbal, and Usman Ali. “Game Chromatic Number of Cartesian and Corona Product Graphs”. Journal of Algebra Combinatorics Discrete Structures and Applications 5, no. 3 (October 2018): 129-36. https://doi.org/10.13069/jacodesmath.458240.
EndNote Bokhary SAUH, Iqbal T, Ali U (October 1, 2018) Game chromatic number of Cartesian and corona product graphs. Journal of Algebra Combinatorics Discrete Structures and Applications 5 3 129–136.
IEEE S. A. U. H. Bokhary, T. Iqbal, and U. Ali, “Game chromatic number of Cartesian and corona product graphs”, Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 5, no. 3, pp. 129–136, 2018, doi: 10.13069/jacodesmath.458240.
ISNAD Bokhary, Syed Ahtsham Ul Haq et al. “Game Chromatic Number of Cartesian and Corona Product Graphs”. Journal of Algebra Combinatorics Discrete Structures and Applications 5/3 (October 2018), 129-136. https://doi.org/10.13069/jacodesmath.458240.
JAMA Bokhary SAUH, Iqbal T, Ali U. Game chromatic number of Cartesian and corona product graphs. Journal of Algebra Combinatorics Discrete Structures and Applications. 2018;5:129–136.
MLA Bokhary, Syed Ahtsham Ul Haq et al. “Game Chromatic Number of Cartesian and Corona Product Graphs”. Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 5, no. 3, 2018, pp. 129-36, doi:10.13069/jacodesmath.458240.
Vancouver Bokhary SAUH, Iqbal T, Ali U. Game chromatic number of Cartesian and corona product graphs. Journal of Algebra Combinatorics Discrete Structures and Applications. 2018;5(3):129-36.