PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2008 | 28 | 2 | 229-247
Tytuł artykułu

Minimal cycle bases of the lexicographic product of graphs

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A construction of minimum cycle bases of the lexicographic product of graphs is presented. Moreover, the length of a longest cycle of a minimal cycle basis is determined.
Słowa kluczowe
Wydawca
Rocznik
Tom
28
Numer
2
Strony
229-247
Opis fizyczny
Daty
wydano
2008
otrzymano
2007-05-23
poprawiono
2008-04-17
zaakceptowano
2008-04-17
Twórcy
  • Department of Mathematics, Yarmouk University, Irbid-Jordan
Bibliografia
  • [1] M. Anderson and M. Lipman, The wreath product of graphs, Graphs and Applications (Boulder, Colo., 1982), (Wiley-Intersci. Publ., Wiley, New York, 1985) 23-39.
  • [2] F. Berger, Minimum Cycle Bases in Graphs (PhD thesis, Munich, 2004).
  • [3] Z. Bradshaw and M.M.M. Jaradat, Minimum cycle bases for direct products of K₂ with complete graphs, Australasian J. Combin. (accepted).
  • [4] W.-K. Chen, On vector spaces associated with a graph, SIAM J. Appl. Math. 20 (1971) 525-529, doi: 10.1137/0120054.
  • [5] D.M. Chickering, D. Geiger and D. HecKerman, On finding a cycle basis with a shortest maximal cycle, Information Processing Letters 54 (1994) 55-58, doi: 10.1016/0020-0190(94)00231-M.
  • [6] L.O. Chua and L. Chen, On optimally sparse cycles and coboundary basis for a linear graph, IEEE Trans. Circuit Theory 20 (1973) 54-76.
  • [7] G.M. Downs, V.J. Gillet, J.D. Holliday and M.F. Lynch, Review of ring perception algorithms for chemical graphs, J. Chem. Inf. Comput. Sci. 29 (1989) 172-187, doi: 10.1021/ci00063a007.
  • [8] R. Hammack, Minimum cycle bases of direct products of bipartite graphs, Australasian J. Combin. 36 (2006) 213-221.
  • [9] R. Hammack, Minimum cycle bases of direct products of complete graphs, Information Processing Letters 102 (2007) 214-218, doi: 10.1016/j.ipl.2006.12.012.
  • [10] W. Imrich and S. Klavžar, Product Graphs: Structure and Recognition (Wiley, New York, 2000).
  • [11] W. Imrich and P. Stadler, Minimum cycle bases of product graphs, Australasian J. Combin. 26 (2002) 233-244.
  • [12] M.M.M. Jaradat, On the basis number and the minimum cycle bases of the wreath product of some graphs I, Discuss. Math. Graph Theory 26 (2006) 113-134, doi: 10.7151/dmgt.1306.
  • [13] M.M.M. Jaradat, M.Y. Alzoubi and E.A. Rawashdeh, The basis number of the Lexicographic product of different ladders, SUT Journal of Mathematics 40 (2004) 91-101.
  • [14] A. Kaveh, Structural Mechanics, Graph and Matrix Methods. Research Studies Press (Exeter, UK, 1992).
  • [15] A. Kaveh and R. Mirzaie, Minimal cycle basis of graph products for the force method of frame analysis, Communications in Numerical Methods in Engineering, to appear, doi: 10.1002/cnm.979.
  • [16] G. Liu, On connectivities of tree graphs, J. Graph Theory 12 (1988) 435-459, doi: 10.1002/jgt.3190120318.
  • [17] M. Plotkin, Mathematical basis of ring-finding algorithms in CIDS, J. Chem. Doc. 11 (1971) 60-63, doi: 10.1021/c160040a013.
  • [18] P. Vismara, Union of all the minimum cycle bases of a graph, Electr. J. Combin. 4 (1997) 73-87.
  • [19] D.J.A. Welsh, Kruskal's theorem for matroids, Proc. Cambridge Phil, Soc. 64 (1968) 3-4, doi: 10.1017/S030500410004247X.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1403
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.