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On the crossing numbers of Cartesian products of stars and paths or cycles. (English) Zbl 0755.05067
Summary: The main results of this paper show that the crossing number of the Cartesian product $$S_ 4\times P_ n$$ is $$2(n-1)$$ for $$n\geq 1$$ and that the crossing number of the Cartesian product $$S_ 4\times C_ n$$ is $$2n$$ for $$n\geq 6$$. We also get the crossing numbers of $$S_ 4\times C_ 3$$, $$S_ 4\times C_ 4$$ and $$S_ 4\times C_ 5$$.

##### MSC:
 05C38 Paths and cycles
##### Keywords:
crossing numbers; Cartesian products; stars; paths; cycles
Full Text:
##### References:
 [1] ERDÖS P., GUY R. K.: Crossing number problems. Amer. Math. Monthly, 80, 1973, 52-58. · Zbl 0264.05109 [2] HARARY F.: Graph Theory. Addison-Wesley, Reading Mass. 1969. · Zbl 0196.27202 [3] JENDROĽ S., ŠČERBOVÁ M.: On the crossing numbers of Sm x Pn, and Sm x Cn. Časopis pro pěstování matematiky, 107, 1982, 225-230. [4] KLEITMAN D. J.: The crossing number of K5. n. J. Combinatorial Theory B, 9, 1970, 315-323. · Zbl 0205.54401 [5] KOMAN M.: On the crossing numbers of graphs. Acta Univ. Carolinae Math. Phys., 10, 1969, 9-46. · Zbl 0256.05103 [6] RINGEISEN R. D., BEINEKE L. W.: The crossing number of C3 x Cn. J. Combinatorial Theory B, 24, 1978, 134- 136. · Zbl 0383.05015 [7] RINGEISEN R. D., BEINEKE L. W.: On the crossing numbers of product of cycles and graphs of order four. J. Graph Theory, 4, 1980, 145-155. · Zbl 0403.05037
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