Minimal cycle bases of the lexicographic product of graphs

M.M.M. Jaradat

Discussiones Mathematicae Graph Theory (2008)

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

Abstract

top
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.

How to cite

top

M.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. [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. [2] F. Berger, Minimum Cycle Bases in Graphs (PhD thesis, Munich, 2004). Zbl1082.05083
  3. [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. [4] W.-K. Chen, On vector spaces associated with a graph, SIAM J. Appl. Math. 20 (1971) 525-529, doi: 10.1137/0120054. 
  5. [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. [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. [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. [8] R. Hammack, Minimum cycle bases of direct products of bipartite graphs, Australasian J. Combin. 36 (2006) 213-221. Zbl1106.05051
  9. [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. [10] W. Imrich and S. Klavžar, Product Graphs: Structure and Recognition (Wiley, New York, 2000). 
  11. [11] W. Imrich and P. Stadler, Minimum cycle bases of product graphs, Australasian J. Combin. 26 (2002) 233-244. Zbl1009.05078
  12. [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. [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. [14] A. Kaveh, Structural Mechanics, Graph and Matrix Methods. Research Studies Press (Exeter, UK, 1992). Zbl0858.73002
  15. [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. [16] G. Liu, On connectivities of tree graphs, J. Graph Theory 12 (1988) 435-459, doi: 10.1002/jgt.3190120318. Zbl0649.05044
  17. [17] M. Plotkin, Mathematical basis of ring-finding algorithms in CIDS, J. Chem. Doc. 11 (1971) 60-63, doi: 10.1021/c160040a013. 
  18. [18] P. Vismara, Union of all the minimum cycle bases of a graph, Electr. J. Combin. 4 (1997) 73-87. Zbl0885.05101
  19. [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 ?

top

You must be logged in to post comments.

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

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.