# Minimal cycle bases of the lexicographic product of graphs

Discussiones Mathematicae Graph Theory (2008)

- Volume: 28, Issue: 2, page 229-247
- ISSN: 2083-5892

## Access Full Article

top## Abstract

top## How to cite

topM.M.M. Jaradat. "Minimal cycle bases of the lexicographic product of graphs." Discussiones Mathematicae Graph Theory 28.2 (2008): 229-247. <http://eudml.org/doc/270507>.

@article{M2008,

abstract = {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.},

author = {M.M.M. Jaradat},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {cycle space; lexicographic product; cycle basis},

language = {eng},

number = {2},

pages = {229-247},

title = {Minimal cycle bases of the lexicographic product of graphs},

url = {http://eudml.org/doc/270507},

volume = {28},

year = {2008},

}

TY - JOUR

AU - M.M.M. Jaradat

TI - Minimal cycle bases of the lexicographic product of graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2008

VL - 28

IS - 2

SP - 229

EP - 247

AB - 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.

LA - eng

KW - cycle space; lexicographic product; cycle basis

UR - http://eudml.org/doc/270507

ER -

## References

top- [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). Zbl1082.05083
- [3] Z. Bradshaw and M.M.M. Jaradat, Minimum cycle bases for direct products of K₂ with complete graphs, Australasian J. Combin. (accepted). Zbl1228.05184
- [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. Zbl0875.68685
- [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. Zbl1106.05051
- [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. Zbl1185.05088
- [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. Zbl1009.05078
- [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. Zbl1104.05036
- [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. Zbl1072.05049
- [14] A. Kaveh, Structural Mechanics, Graph and Matrix Methods. Research Studies Press (Exeter, UK, 1992). Zbl0858.73002
- [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. Zbl1159.70344
- [16] G. Liu, On connectivities of tree graphs, J. Graph Theory 12 (1988) 435-459, doi: 10.1002/jgt.3190120318. Zbl0649.05044
- [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. Zbl0885.05101
- [19] D.J.A. Welsh, Kruskal's theorem for matroids, Proc. Cambridge Phil, Soc. 64 (1968) 3-4, doi: 10.1017/S030500410004247X. Zbl0157.55302

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.