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2013 | 33 | 3 | 571-582
Tytuł artykułu

The Crossing Numbers of Products of Path with Graphs of Order Six

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The crossing numbers of Cartesian products of paths, cycles or stars with all graphs of order at most four are known. For the path Pn of length n, the crossing numbers of Cartesian products G⃞Pn for all connected graphs G on five vertices are also known. In this paper, the crossing numbers of Cartesian products G⃞Pn for graphs G of order six are studied. Let H denote the unique tree of order six with two vertices of degree three. The main contribution is that the crossing number of the Cartesian product H⃞Pn is 2(n − 1). In addition, the crossing numbers of G⃞Pn for fourty graphs G on six vertices are collected
Słowa kluczowe
Wydawca
Rocznik
Tom
33
Numer
3
Strony
571-582
Opis fizyczny
Daty
wydano
2013-07-01
online
2013-07-30
Twórcy
  • Faculty of Electrical Engineering and Informatics Technical University of Košice Letná 9, 042 00 Košice, Slovak Republic, marian.klesc@tuke.sk
  • Faculty of Electrical Engineering and Informatics Technical University of Košice Letná 9, 042 00 Košice, Slovak Republic, jana.petrillova@tuke.sk
Bibliografia
  • [1] L.W. Beineke and R.D. Ringeisen, On the crossing numbers of products of cycles and graphs of order four , J. Graph Theory 4 (1980) 145-155. doi:10.1002/jgt.3190040203[Crossref]
  • [2] D. Bokal, On the crossing number of Cartesian products with paths, J. Combin. Theory (B) 97 (2007) 381-384. doi:10.1016/j.jctb.2006.06.003[Crossref]
  • [3] S. Jendrol’ and M. Ščerbová, On the crossing numbers of Sm × Pn and Sm × Cn, ˇ Casopis Pro P ˇ estov´ an´ı Matematiky 107 ( 1982) 225-230.
  • [4] M. Klešč, The crossing numbers of Cartesian products of stars and paths or cycles, Math. Slovaca 41 (1991) 113-120.
  • [5] M. Klešč, The crossing numbers of products of paths and stars with 4-vertex graphs, J. Graph Theory 18 (1994) 605-614.
  • [6] M. Klešč, The crossing number of K2,3 ×Pn and K2,3 ×Sn, Tatra Mt. Math. Publ. 9 (1996) 51-56.
  • [7] M. Klešč, The crossing numbers of products of 4-vertex graphs with paths and cycles, Discuss. Math. Graph Theory 19 (1999) 59-69. doi:10.7151/dmgt.1085[Crossref]
  • [8] M. Klešč, The crossing numbers of Cartesian products of paths with 5-vertex graphs, Discrete Math. 233 (2001) 353-359. doi:10.1016/S0012-365X(00)00251-X[Crossref][WoS]
  • [9] D. Kravecová, The crossing number of P2 5 × Pn, Creat. Math. Inform. 28 (2012) 49-56.
  • [10] Y.H. Peng and Y.C. Yiew, The crossing number of P(3, 1)×Pn, Discrete Math. 306 (2006) 1941-1946. doi:10.1016/j.disc.2006.03.058[Crossref]
  • [11] J. Wang and Y. Huang, The crossing number of K2,4 ×Pn, Acta Math. Sci.,Ser. A, Chin. Ed. 28 (2008) 251-255.
  • [12] L. Zhao, W. He, Y. Liu and X. Ren, The crossing number of two Cartesian products, Int. J. Math. Comb. 1 (2007) 120-127.
  • [13] W. Zheng, X. Lin, Y. Yang and Ch. Cui, On the crossing number of Km⃞Pn, Graphs Combin. 23 (2007) 327-336. doi:10.1007/s00373-007-0726-z [Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_7151_dmgt_1684
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