The (2,1) -Total Labeling of Sn+1∨Pm and Sn+1×Pm

ABSTRACT

The (2,1)-total labeling number of a graph is the width of the smallest range of integers that suffices to label the vertices and the edges of such that no two adjacent vertices have the same label, no two adjacent edges have the same label and the difference between the labels of a vertex and its incident edges is at least 2. In this paper, we studied the upper bound of of Sn+1∨Pm and Sn+1×Pm

The (2,1)-total labeling number of a graph is the width of the smallest range of integers that suffices to label the vertices and the edges of such that no two adjacent vertices have the same label, no two adjacent edges have the same label and the difference between the labels of a vertex and its incident edges is at least 2. In this paper, we studied the upper bound of of Sn+1∨Pm and Sn+1×Pm

Cite this paper

nullS. Zhang, Q. Ma and J. Wang, "The (2,1) -Total Labeling of Sn+1∨Pm and Sn+1×Pm,"*Applied Mathematics*, Vol. 1 No. 5, 2010, pp. 366-369. doi: 10.4236/am.2010.15048.

nullS. Zhang, Q. Ma and J. Wang, "The (2,1) -Total Labeling of Sn+1∨Pm and Sn+1×Pm,"

References

[1] J. A. Bondy and U. S. R. Murty, “Graph Theory with Applications,” MacMillan, London, 1976.

[2] J. R. Griggs and R. K. Yeh, “Labeling Graphs with a Condition at Distance 2,” SIAM Journal on Discrete Mathematics, Vol. 5, No. 1, 1992, pp. 586-595.

[3] M. A. Whittlesey, J. P. Georges and D. W. Mauro, “On the -Number of and Related Graphs,” IAM Journal on Discrete Mathematics, Vol. 8, No. 1, 1995, pp. 499-506.

[4] F. Havet and M. Yu, “ -Total Labeling of Graph, Technical Report 4650,” INRIA, Sophia Antipolis, 2002.

[5] O. V. Borodin, A. V. Kostochka and D. R. Woodall, “List Edge and List Total Coloring of Multigraphs,” Journal of Combinatorial Theory, Series B, Vol. 71, 1997, pp. 184- 204.

[6] M. Molloy and B. Reed, “A Bound on the Total Chromatic Number,” Combinatorics, Vol. 18, No. 2, 1998, pp. 241-280.

[7] W. F. Wang, “Total Chromatic Number of Planar Graphs with Maximum Degree Ten,” Journal of Graph Theory, Vol. 54, No. 1, 2007, pp. 91-102.

[8] D. Chen and W. F. Wang, “ -Total Labeling of Outerplanar Graphs,” Discrete Applied Mathematics, Vol. 155, No. 18, 2007, pp. 2585-2593.

[9] M. Montassier and A. Raspaud, “ -Total Labeling of Graphs with a Given Maximum Average Degree,” Journal of Graph Theory, Vol. 51, 2006, pp. 93-109.

[10] S. M. Zhang and K. Pan, “The -Total Labeling of ,” Journal of University of Jinan, Vol. 23, No. 3, 2009, pp. 308-311.

[11] S. M. Zhang and Q. L. Ma, “The -Total Labeling of ,” Journal of Shandong University (Nature Science), Vol. 42, No. 3, 2009, pp. 39-43.

[1] J. A. Bondy and U. S. R. Murty, “Graph Theory with Applications,” MacMillan, London, 1976.

[2] J. R. Griggs and R. K. Yeh, “Labeling Graphs with a Condition at Distance 2,” SIAM Journal on Discrete Mathematics, Vol. 5, No. 1, 1992, pp. 586-595.

[3] M. A. Whittlesey, J. P. Georges and D. W. Mauro, “On the -Number of and Related Graphs,” IAM Journal on Discrete Mathematics, Vol. 8, No. 1, 1995, pp. 499-506.

[4] F. Havet and M. Yu, “ -Total Labeling of Graph, Technical Report 4650,” INRIA, Sophia Antipolis, 2002.

[5] O. V. Borodin, A. V. Kostochka and D. R. Woodall, “List Edge and List Total Coloring of Multigraphs,” Journal of Combinatorial Theory, Series B, Vol. 71, 1997, pp. 184- 204.

[6] M. Molloy and B. Reed, “A Bound on the Total Chromatic Number,” Combinatorics, Vol. 18, No. 2, 1998, pp. 241-280.

[7] W. F. Wang, “Total Chromatic Number of Planar Graphs with Maximum Degree Ten,” Journal of Graph Theory, Vol. 54, No. 1, 2007, pp. 91-102.

[8] D. Chen and W. F. Wang, “ -Total Labeling of Outerplanar Graphs,” Discrete Applied Mathematics, Vol. 155, No. 18, 2007, pp. 2585-2593.

[9] M. Montassier and A. Raspaud, “ -Total Labeling of Graphs with a Given Maximum Average Degree,” Journal of Graph Theory, Vol. 51, 2006, pp. 93-109.

[10] S. M. Zhang and K. Pan, “The -Total Labeling of ,” Journal of University of Jinan, Vol. 23, No. 3, 2009, pp. 308-311.

[11] S. M. Zhang and Q. L. Ma, “The -Total Labeling of ,” Journal of Shandong University (Nature Science), Vol. 42, No. 3, 2009, pp. 39-43.