Crossing Numbers of Certain Graphs

Since Harary, Kainen and Schwenk conjectured in 1973 that the crossing number of the Cartesian product of an m-cycle with an n-cycle is for , many results on the crossing number of the Cartesian product of graphs have been obtained. In this thesis, we study and investigate the crossing numbers of and. The thesis begins with an explanation of the necessary terminology. The thesis continues by finding the crossing number of and . We show that the crossing number of is for . We then proved that the crossing number of is for . We end the thesis by investigating the crossing number of . We also show that, the crossing number of is . The determination of the crossing number of for is left as an open problem for future research.

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