Yıl 2018, Cilt 5, Sayı 3, Sayfalar 129 - 136 2018-10-08

Game chromatic number of Cartesian and corona product graphs

Syed Ahtsham Ul Haq Bokhary [1] , Tanveer Iqbal [2] , Usman Ali [3]

16 47

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 $P_{m}\circ C_{n}$.
Game chromatic number, Cartesian product, Corona product
  • [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.
Birincil Dil en
Konular Mühendislik
Dergi Bölümü Makaleler
Yazarlar

Yazar: Syed Ahtsham Ul Haq Bokhary (Sorumlu Yazar)

Yazar: Tanveer Iqbal

Yazar: Usman Ali

Bibtex @araştırma makalesi { jacodesmath458240, journal = {Journal of Algebra Combinatorics Discrete Structures and Applications}, issn = {}, eissn = {2148-838X}, address = {Yıldız Teknik Üniversitesi}, year = {2018}, volume = {5}, pages = {129 - 136}, doi = {10.13069/jacodesmath.458240}, title = {Game chromatic number of Cartesian and corona product graphs}, key = {cite}, author = {Ali, Usman and Iqbal, Tanveer and Bokhary, Syed Ahtsham Ul Haq} }
APA Bokhary, S , 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. DOI: 10.13069/jacodesmath.458240
MLA Bokhary, S , Iqbal, T , Ali, U . "Game chromatic number of Cartesian and corona product graphs". Journal of Algebra Combinatorics Discrete Structures and Applications 5 (2018): 129-136 <http://dergipark.gov.tr/jacodesmath/issue/16096/458240>
Chicago Bokhary, S , Iqbal, T , Ali, U . "Game chromatic number of Cartesian and corona product graphs". Journal of Algebra Combinatorics Discrete Structures and Applications 5 (2018): 129-136
RIS TY - JOUR T1 - Game chromatic number of Cartesian and corona product graphs AU - Syed Ahtsham Ul Haq Bokhary , Tanveer Iqbal , Usman Ali Y1 - 2018 PY - 2018 N1 - doi: 10.13069/jacodesmath.458240 DO - 10.13069/jacodesmath.458240 T2 - Journal of Algebra Combinatorics Discrete Structures and Applications JF - Journal JO - JOR SP - 129 EP - 136 VL - 5 IS - 3 SN - -2148-838X M3 - doi: 10.13069/jacodesmath.458240 UR - http://dx.doi.org/10.13069/jacodesmath.458240 Y2 - 2018 ER -
EndNote %0 Journal of Algebra Combinatorics Discrete Structures and Applications Game chromatic number of Cartesian and corona product graphs %A Syed Ahtsham Ul Haq Bokhary , Tanveer Iqbal , Usman Ali %T Game chromatic number of Cartesian and corona product graphs %D 2018 %J Journal of Algebra Combinatorics Discrete Structures and Applications %P -2148-838X %V 5 %N 3 %R doi: 10.13069/jacodesmath.458240 %U 10.13069/jacodesmath.458240
ISNAD Bokhary, Syed Ahtsham Ul Haq , Iqbal, Tanveer , Ali, Usman . "Game chromatic number of Cartesian and corona product graphs". Journal of Algebra Combinatorics Discrete Structures and Applications 5 / 3 (Ekim 2018): 129-136. http://dx.doi.org/10.13069/jacodesmath.458240