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, Tome 26 (2006), p. 113-134 / Harvested from The Polish Digital Mathematics Library

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.

Publié le : 2006-01-01
EUDML-ID : urn:eudml:doc:270783
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1306,
     author = {Mohammed M.M. Jaradat},
     title = {On the basis number and the minimum cycle bases of the wreath product of some graphs i},
     journal = {Discussiones Mathematicae Graph Theory},
     volume = {26},
     year = {2006},
     pages = {113-134},
     zbl = {1104.05036},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1306}
}
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, Tome 26 (2006) pp. 113-134. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1306/

[000] [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.

[001] [2] A.A. Ali, The basis number of complete multipartite graphs, Ars Combin. 28 (1989) 41-49. | Zbl 0728.05058

[002] [3] A.A. Ali, The basis number of the direct product of paths and cycles, Ars Combin. 27 (1989) 155-163.

[003] [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. | Zbl 0880.05055

[004] [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. | Zbl 0958.05074

[005] [6] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (America Elsevier Publishing Co. Inc., New York, 1976). | Zbl 1226.05083

[006] [7] W.-K. Chen, On vector spaces associated with a graph, SIAM J. Appl. Math. 20 (1971) 525-529, doi: 10.1137/0120054.

[007] [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. | Zbl 0875.68685

[008] [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.

[009] [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.

[010] [11] W. Imrich and S. Klavžar, Product Graphs: Structure and Recognition (Wiley, New York, 2000).

[011] [12] W. Imrich and P. Stadler, Minimum cycle bases of product graphs, Australas. J. Combin. 26 (2002) 233-244. | Zbl 1009.05078

[012] [13] M.M.M. Jaradat, On the basis number of the direct product of graphs, Australas. J. Combin. 27 (2003) 293-306. | Zbl 1021.05060

[013] [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. | Zbl 1074.05051

[014] [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. | Zbl 1107.05049

[015] [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. | Zbl 1072.05049

[016] [17] A. Kaveh, Structural Mechanics, Graph and Matrix Methods. Research Studies Press (Exeter, UK, 1992). | Zbl 0858.73002

[017] [18] G. Liu, On connectivities of tree graphs, J. Graph Theory 12 (1988) 435-459, doi: 10.1002/jgt.3190120318. | Zbl 0649.05044

[018] [19] S. MacLane, A combinatorial condition for planar graphs, Fundamenta Math. 28 (1937) 22-32. | Zbl 0015.37501

[019] [20] M. Plotkin, Mathematical basis of ring-finding algorithms in CIDS, J. Chem. Doc. 11 (1971) 60-63, doi: 10.1021/c160040a013.

[020] [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. | Zbl 0385.05031

[021] [22] P. Vismara, Union of all the minimum cycle bases of a graph, Electr. J. Combin. 4 (1997) 73-87. | Zbl 0885.05101

[022] [23] D.J.A. Welsh, Kruskal's theorem for matroids, Proc. Cambridge Phil, Soc. 64 (1968) 3-4, doi: 10.1017/S030500410004247X. | Zbl 0157.55302