Paper title:

The L(2,1)-Labeling of Some Middle Graphs

Published in: Issue 3, (Vol. 4) / 2010
Publishing date: 2010-10-26
Pages: 104-107
Author(s): VAIDYA Samir K., BANTVA Devsi D.
Abstract. An (2,1) L -labeling of a graph G is a function f from the vertex set V (G) to the set of all nonnegative integers such that |f(x)-f(y)| >= 2 if d(x,y) = 1 and |f(x)-f(y)| >= 1 if if d(x,y) = 2. The L(2,1) -labeling number λ(G) of G is the smallest number k such that G has an L(2,1)-labeling with max{f(v): v∈ V(G). In this paper we completely determine λ-number for middle graph of path Pn, cycle Cn , star K1,n, friendship graph F nand wheel Wn.
Keywords: L (2,1) -labeling, λ Number, Middle Graphs.

1. G. J. Chang and D. Kuo, The L(2,1) -labeling problem on graphs, SIAM J. Discrete Math. 9(2)(1996), pp.309-316.

2. J. Georges and D. Mauro, Generalized vertex labelings with a condition at distance two, Congr. Numer. 109(1995), pp.141- 159.

3. J. Georges, D. Mauro and M. Whittlesey, Relating path covering to vertex labelings with a condition at distance two, Discrete Math. 135(1994), pp.103-111.

4. J. R. Griggs and R. K. Yeh, Labeling graphs with a condition at distance 2, SIAM J. Discrete Math. 5(1992), pp.586-595.

5. W. K. Hale, Frequency assignment: Theory and applications, Proc. IEEE, 68(1980), pp.1497-1514.

6. D. Sakai, Labeling chordal graphs: Distance two condition, SIAM J. Discrete Math. 7(1)(1994), pp.133-140.

7. S. K. Vaidya, P. L. Vihol, N. A. Dani, D. D. Bantva, L(2,1) - labeling in the context of some graph operations, Journal of Mathematics Research, 2(3)(2010), pp. 109-119.

8. D. B. West, Introduction to Graph Theory, Prentice-Hall of India, 2001.

9. R. K. Yeh, Labeling graphs with a condition at distance two, Ph. D. Thesis, Dept. of Math., University of South Carolina, Columbia, SC, 1990.

Back to the journal content
Creative Commons License
This article is licensed under a
Creative Commons Attribution-ShareAlike 4.0 International License.
Home | Editorial Board | Author info | Archive | Contact
Copyright JACSM 2007-2023