Discussiones Mathematicae Graph Theory 29(3) (2009)
481-498
doi: 10.7151/dmgt.1459
Lixia Fan and Zhihe Liang
Department of Mathematics, Hebei Normal University
Shijiazhuang 050016, P.R. China
e-mail: zhiheliang@163.com.cn
Keywords: permutation graph; graceful, Lee's conjecture.
2000 Mathematics Subject Classification: 05C78.
[1] | A. Rosa, On certain valuations of the vertices of a graph, in: Theory of Graphs, Proc. of Intemational Symposium, Rome 1966 (Gordon Breach, New York 1967), 349-355. |
[2] | S.W. Golomb, How to number a graph? in: R.C. Read, ed., Graph Theory and Computing (Academic Press, New York, 1972) 23-27. |
[3] | Z. Liang, On the graceful conjecture of permutation graphs of paths, Ars Combin. 91 (2009) 65-82. |
[4] | J.A. Gallian, A dynamic survey of graph labeling, Electronic J. Combin. 14 (2007) DS#6, 1-180. |
[5] | J.C. Bermond, Graceful graphs, radio antennae and Fench windmills, in: R.J. Wilson, ed., Graph Theory and Combinatorics (Pitman, London, 1979), 13-37. |
[6] | A.K. Dewdney, The search for an invisible ruler that will help radio astronomers to measure the earth, Scientific American, Dec. (1986) 16-19, doi: 10.1038/scientificamerican0186-16. |
[7] | S.M. Lee, K.Y. Lai, Y.S. Wang and M.K. Kiang, On the graceful permutation graphs conjecture, Congr. Numer. 103 (1994) 193-201. |
[8] | M. Maheo, Strongly graceful graphs, Discrete Math. 29 (1980) 39-46, doi: 10.1016/0012-365X(90)90285-P. |
[9] | C. Delorme, Two sets of graceful graphs, J. Graph Theory 4 (1980) 247-250, doi: 10.1002/jgt.3190040214. |
[10] | R.W. Frucht and J.A. Gallian, Labelling prisms, Ars Combin. 26 (1988) 69-82. |
[11] | J.A. Gallian, Labelling prisms and prism related graphs, Congress. Numer. 59 (1987) 89-100. |
[12] | Z. Liang, H. Zhang, N. Xu, S. Ye, Y. Fan and H. Ge, Gracefulness of five permutation graphs of paths, Utilitas Mathematica 72 (2007) 241-249. |
[13] | N. Han and Z. Liang, On the graceful permutation graphs conjecture, J. Discrete Math. Sci. & Cryptography 11 (2008) 501-526. |
Received 13 November 2007
Revised 21 April 2009
Accepted 4 June 2009