Igra sparivanja na konačnim podgrafovima pravilnih rešetki

Pijević, Marija (2014) Igra sparivanja na konačnim podgrafovima pravilnih rešetki. Diploma thesis, Faculty of Science > Department of Mathematics.

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Abstract

In this graduate thesis we found winning strategies for some forms of hexagonal animals. At the beginning, we have provided the basic concepts of combinatorial game theory and theory of graphs which was necessary for analysing the thesis. After that, we pointed out some forms of hexagonal animals on which we will make matching games and we explained the difference between symmetries $C_i$ and $D_i, i = 1, 2, 3, 6$. The last chapter was dedicated to analysis of some symmetries. First, we played matching game on the chain polihexes. We have seen that the winner may be the first or the second player, depending on whether the chain hexagonal animal is made up of even or odd number of hexagons. After that, we analyzed symmetries $C_6$and $D_6$ and saw that always wins only the second player. Symmetries $C_2$ and $D_2$ have winning strategies for both players. We made analysis of symmetry $D_1$ quite extensively and showed that the winner can be any player. Symmetry $C_1$ is not very interesting, so we played only one game and saw that the winner is first player. Graphs of symmetry $D_3$, on which we played matching game, give victory to the second player. For symmetry $C_3$ we pointed out two graphs, but we didn’t played matching game because it is quite complicated. After all that, we came to a conclusion. In a game in which center of symmetry is located in the center of the central hexagon, the winner is always the second player. If the center of symmetry is at midpoint of an edge, the winner is always the first player.

Item Type: Thesis (Diploma thesis)
Supervisor: Došlić, Tomislav
Date: 2014
Number of Pages: 42
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 17 Jun 2015 09:49
Last Modified: 17 Jun 2015 09:49
URI: http://digre.pmf.unizg.hr/id/eprint/4054

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