On the basis number and the minimum cycle bases of the wreath product of some graphs i

Mohammed M.M. Jaradat

Discussiones Mathematicae Graph Theory (2006)

  • Volume: 26, Issue: 1, page 113-134
  • ISSN: 2083-5892

Abstract

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A construction of a minimum cycle bases for the wreath product of some classes of graphs is presented. Moreover, the basis numbers for the wreath product of the same classes are determined.

How to cite

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Mohammed M.M. Jaradat. "On the basis number and the minimum cycle bases of the wreath product of some graphs i." Discussiones Mathematicae Graph Theory 26.1 (2006): 113-134. <http://eudml.org/doc/270783>.

@article{MohammedM2006,
abstract = {A construction of a minimum cycle bases for the wreath product of some classes of graphs is presented. Moreover, the basis numbers for the wreath product of the same classes are determined.},
author = {Mohammed M.M. Jaradat},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {cycle space; basis number; cycle basis; wreath product},
language = {eng},
number = {1},
pages = {113-134},
title = {On the basis number and the minimum cycle bases of the wreath product of some graphs i},
url = {http://eudml.org/doc/270783},
volume = {26},
year = {2006},
}

TY - JOUR
AU - Mohammed M.M. Jaradat
TI - On the basis number and the minimum cycle bases of the wreath product of some graphs i
JO - Discussiones Mathematicae Graph Theory
PY - 2006
VL - 26
IS - 1
SP - 113
EP - 134
AB - A construction of a minimum cycle bases for the wreath product of some classes of graphs is presented. Moreover, the basis numbers for the wreath product of the same classes are determined.
LA - eng
KW - cycle space; basis number; cycle basis; wreath product
UR - http://eudml.org/doc/270783
ER -

References

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  1. [1] M. Anderson and M. Lipman, The wreath product of graphs, in: Graphs and Applications (Boulder, Colo., 1982), (Wiley-Intersci. Publ., Wiley, New York, 1985) 23-39. 
  2. [2] A.A. Ali, The basis number of complete multipartite graphs, Ars Combin. 28 (1989) 41-49. Zbl0728.05058
  3. [3] A.A. Ali, The basis number of the direct product of paths and cycles, Ars Combin. 27 (1989) 155-163. 
  4. [4] A.A. Ali and G.T. Marougi, The basis number of cartesian product of some graphs, J. Indian Math. Soc. 58 (1992) 123-134. Zbl0880.05055
  5. [5] A.S. Alsardary and J. Wojciechowski, The basis number of the powers of the complete graph, Discrete Math. 188 (1998) 13-25, doi: 10.1016/S0012-365X(97)00271-9. Zbl0958.05074
  6. [6] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (America Elsevier Publishing Co. Inc., New York, 1976). Zbl1226.05083
  7. [7] W.-K. Chen, On vector spaces associated with a graph, SIAM J. Appl. Math. 20 (1971) 525-529, doi: 10.1137/0120054. 
  8. [8] D.M. Chickering, D. Geiger and D. HecKerman, On finding a cycle basis with a shortest maximal cycle, Inform. Process. Lett. 54 (1994) 55-58, doi: 10.1016/0020-0190(94)00231-M. Zbl0875.68685
  9. [9] 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. 
  10. [10] 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. 
  11. [11] W. Imrich and S. Klavžar, Product Graphs: Structure and Recognition (Wiley, New York, 2000). 
  12. [12] W. Imrich and P. Stadler, Minimum cycle bases of product graphs, Australas. J. Combin. 26 (2002) 233-244. Zbl1009.05078
  13. [13] M.M.M. Jaradat, On the basis number of the direct product of graphs, Australas. J. Combin. 27 (2003) 293-306. Zbl1021.05060
  14. [14] M.M.M. Jaradat, The basis number of the direct product of a theta graph and a path, Ars Combin. 75 (2005) 105-111. Zbl1074.05051
  15. [15] M.M.M. Jaradat, An upper bound of the basis number of the strong product of graphs, Discuss. Math. Graph Theory 25 (2005) 391-406, doi: 10.7151/dmgt.1291. Zbl1107.05049
  16. [16] M.M.M. Jaradat, M.Y. Alzoubi and E.A. Rawashdeh, The basis number of the Lexicographic product of different ladders, SUT J. Math. 40 (2004) 91-101. Zbl1072.05049
  17. [17] A. Kaveh, Structural Mechanics, Graph and Matrix Methods. Research Studies Press (Exeter, UK, 1992). Zbl0858.73002
  18. [18] G. Liu, On connectivities of tree graphs, J. Graph Theory 12 (1988) 435-459, doi: 10.1002/jgt.3190120318. Zbl0649.05044
  19. [19] S. MacLane, A combinatorial condition for planar graphs, Fundamenta Math. 28 (1937) 22-32. Zbl0015.37501
  20. [20] M. Plotkin, Mathematical basis of ring-finding algorithms in CIDS, J. Chem. Doc. 11 (1971) 60-63, doi: 10.1021/c160040a013. 
  21. [21] E.F. Schmeichel, The basis number of a graph, J. Combin. Theory (B) 30 (1981) 123-129, doi: 10.1016/0095-8956(81)90057-5. Zbl0385.05031
  22. [22] P. Vismara, Union of all the minimum cycle bases of a graph, Electr. J. Combin. 4 (1997) 73-87. Zbl0885.05101
  23. [23] D.J.A. Welsh, Kruskal's theorem for matroids, Proc. Cambridge Phil, Soc. 64 (1968) 3-4, doi: 10.1017/S030500410004247X. Zbl0157.55302

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