L (2, 1)-labeling of direct product of paths and cycles

Discrete Applied Mathematics

Volumn 145, Issue 2, 2005, Pages 317-325

  Jha, Pranava K ^a   Klavžar, Sandi ^b   Vesel, Aleksander ^b  

^a ST CLOUD STATE UNIVERSITY   (United States)

^b UNIVERSITY OF MARIBOR   (Slovenia)

Author keywords

number; Channel assignment; Direct product of graphs; Dynamic algorithm; Fasciagraph; L(2, 1) labeling; Rotagraph; Vertex labeling

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; CONSTRAINT THEORY; NUMBER THEORY; PROBLEM SOLVING; RANDOM PROCESSES; SET THEORY;

Λ-NUMBER; CHANNEL ASSIGNMENT; DIRECT PRODUCT OF GRAPHS; DYNAMIC ALGORITHMS; FASCIGRAPH; L(2,1)-LABELING; ROTAGRAPH; VERTEX LABELING;

GRAPH THEORY;

EID: 8344267498     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2004.01.019     Document Type: Article

References (31)

1. D. Babić, A. Graovac, B. Mohar, T. Pisanski, The matching polynomial of a polygraph, Discrete Appl. Math. 15 (1986) 11-24.
2. G.J. Chang, D. Kuo, The L(2,1)-Labeling on graphs, SIAM J. Discrete Math. 9 (1996) 309-316.
3. J. Fiala, T. Kloks, J. Kratochvil, Fixed-parameter complexity of λ-labelings, Discrete Appl. Math. 113 (2001) 59-72.
4. J. Georges, D.W. Mauro, Generalized vertex labelings with a condition at distance two, Congr. Numer. 109 (1995) 141-159.
5. J. Georges, D.W. Mauro, On the size of graphs labeled with a condition at distance two, J. Graph Theory 22 (1996) 47-57.
6. j-numbers of the products of complete graphs, Congr. Numer. 140 (1999) 141-160.
7. J.P. Georges, D.W. Mauro, M.L Stein, Labeling products of complete graphs with a condition at distance two, SIAM J. Discrete Math. 14 (2001) 28-35.
8. J.P. Georges, D.W. Mauro, M.A. Whittlesey, Relating path coverings to vertex labellings with a condition at distance two, Discrete Math. 135 (1994) 103-111.
9. J.R. Griggs, R.K. Yen, Labelling graphs with a condition at distance two, SIAM J. Discrete Math. 5 (1992) 586-595.
10. W.K. Hale, Frequency assignment: theory and application, Proc. IEEE 68 (1980) 1497-1514.
11. W. Imrich, S. Klavžar, Product Graphs: Structure and Recognition, Wiley, New York, 2000.
12. P.K. Jha, Optimal L(2,1)-labeling of Cartesian products of cycles, with an application to independent domination, IEEE Trans. Circuits and Systems-I: Fund. Theory and Appl. 47 (2000) 1531-1534.
13. P.K. Jha, Optimal L(2,1)-labeling of Strong products of cycles, IEEE Trans. Circuits and Systems-I: Fund. Theory and Appl. 48 (2001) 498-500.
14. P.K. Jha, Smallest independent dominating sets in Kronecker products of cycles, Discrete Appl. Math. 113 (2001) 303-306.
15. P.K. Jha, A. Narayanan, P. Sood, K. Sundaram, V. Sunder, On L(2,1)-labeling of the Cartesian product of a cycle and a path, Ars Combin. 55 (2000) 81-89.
16. D.S. Johnson, M. Trick (Eds.), Cliques, Coloring and Satisfiability, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 26, American Mathematical Society, Providence, RI, 1996 (DIMACS coloring benchmarks available via ftp at rutgers.dimacs.edu).
17. M. Juvan, B. Mohar, J. Žerovnik, Distance-related invariants on polygraphs, Discrete Appl. Math. 80 (1997) 57-71.
18. S.Klavžar, A. Vesel, Computing graph invariants on rotagraph using dynamic algorithm approach: the case of (2,1)-colorings and independence numbers, Discrete Appl. Math. 129 (2003) 449-460.
19. S. Klevžar, J. Žerovnik, Algebraic approach to fasciagraphs and rotagraphs, Discrete Appl. Math. 68 (1996) 93-100.
20. D. Liu, R.K. Yeh, On distance-two labelings of graphs, Ars Combin. 47 (1997) 13-22.
21. A.D. Petford, D.J.A. Welsh, A randomized 3-colouring algorithm, Discrete Math. 74 (1989) 253-261.
22. J. Ramirez, R. Melhem, Computational arrays with flexible redundancy, Computer 20 (1987) 55-65.
23. F.S. Roberts, T-colorings of graphs: recent results and open problems, Discrete Math. 93 (1991) 229-245.
24. D. Sakai, Labeling chordal graphs: distance-two condition, SIAM J. Discrete Math. 7 (1994) 133-140.
25. J. Shawe-Tayloc J. Žerovnik, Analysis of the mean field annealing algorithm for graph colouring, J. Artif. Neural Networ. 2 (1995) 329-340.
26. K.W. Tang, S.A. Padubirdi, Diagonal and toroidal mesh networks, IEEE Trans. Comput. 43 (1994) 815-826.
27. S. Ubéda, J. Žerovnik, A randomized algorithm for graph coloring applied tn channel assignment problem, in: V. Ropnik, L-Zadnik Stirn, S. Drobne (Eds.), Proceedings of the Fourth International Symposium on Operational Research, Slovenian Society INFORMATIKA - Section for Operational Research, Ljubljana, 1997, pp. 361-366.
28. J. Van den Heuvel, R.A. Leese, M.A. Shepherd, Graph labeling and radio channel assignment, J. Graph Theory 29 (1998) 263-283.
29. 7, Inform. Process. Lett. 81 (2002) 277-282.
30. n and related graphs, SIAM J. Discrete Math. 8 (1995) 499-506.
31. J. Žerovnik, Deriving formulas for domination numbers of fasciagraphs and rotagraphs, in: G. Ciobanu, G. Páun (Eds.), Fundamentals of Computation Theory, Lecture Notes in Computer Science, vol. 1684, Springer, Berlin, 1999, pp. 559-568.