Deriving formulas for domination numbers of fasciagraphs and rotagraphs ?

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1684, Issue , 1999, Pages 559-568

  Žerovnik, Janez ^a,b  

^a UNIVERSITY OF MARIBOR   (Slovenia)

^b INSTITUTE OF MATHEMATICS   (Slovenia)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; COMPUTER SCIENCE; COMPUTERS;

ALGEBRAIC APPROACHES; CONSTANT TIME; DECISION PROBLEMS; DISTANCE-BASED; DOMINATION NUMBER; GRAPH INVARIANT; GRID GRAPHS; VLSI SYSTEM;

COMPUTATION THEORY;

EID: 84956855195     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-48321-7_47     Document Type: Conference Paper

References (33)

1. S. Arnborg, Efficient algorithms for combinatorial problems on graphs with bounded decomposability - a survey, BIT 25 (1985) 2-23.
2. S. Arnborg and A. Proskurowski, Linear time algorithms for NP-hard problems on graphs embedded in k-trees, TRITA-NA-8404, Dept. of Num. Anal. and Comp. Sci, Royal Institute of Technology, Stockholm, Sweden (1984).
3. D. Babić, A. Graovac, B. Mohar and T. Pisanski, The matching polynomial of a polygraph, Discrete Appl. Math. 15 (1986) 11-24.
4. F. Baccelli, G. Cohen, G. J. Olsder and J. P. Quadrat, Synchronization and Linearity (Wiley, 1992).
5. B. Carré, Graphs and Networks (Clarendon Press, Oxford, 1979).
6. T.Y. Chang, Domination Numbers of Grid GRaphs, Ph.D. Thesis, Dept. of Mathematics, Univ. of South Florida, 1992.
7. T.Y. Chang and W.E. Clark, The domination numbers of the 5 × n and 6 × n grid graphs, J. Graph Theory 17 (1993) 81-107.
8. B.N. Clark, C.J. Colbourn and D.S. Johnson, Unit disc graphs, Discrete Math. 86 (1990) 165-177.
9. E.J. Cockayne, E.O. Hare, S.T. Hedetniemi and T.V. Wimer, Bounds for the domination number of grid graphs, Congr. Numer. 47 (1985) 217-228.
10. D.C. Fisher, The domination number of complete grid graphs, J. Graph Theory, submitted.
11. A. Graovac, M. Juvan, B. Mohar, S. Vesel and J. Žerovnik, The Szeged index of polygraphs, in preparation.
12. A. Graovac, M. Juvan, B. Mohar and J. Žerovnik, Computing the determinant and the algebraic structure count on polygraphs, submitted.
13. S. Gravier and M. Mollard, On domination numbers of Cartesian product of paths, Discrete Appl. Math. 80 (1997) 247-250.
14. I. Gutman, N. Kolaković, A. Graovac and D. Babić, A method for calculation of the Hosoya index of polymers, in: A. Graovac, ed., Studies in Physical and Theoretical Chemistry, vol. 63 (Elsevier, Amsterdam, 1989) 141-154.
15. I. Gutman, Formula for the Wiener Number of trees and its extension to graphs containing cycles, Graph Theory Notes New York 27 (1994) 9-15.
16. E.O. Hare, S.T. Hedetniemi and W.R. Hare, Algorithms for computing the domination number of k × n complete grid graphs, Congr. Numer. 55 (1986) 81-92.
17. S.T. Hedetniemi and R.C. Laskar, Introduction, Discrete Math. 86 (1990) 3-9.
18. M.S. Jacobson and L.F. Kinch, On the domination number of products of graphs: I, Ars Combin. 18 (1983) 33-44.
19. M.S. Jacobson and L.F. Kinch, On the domination of the products of graphs II: trees, J. Graph Theory 10 (1986) 97-106.
20. M. Juvan, B. Mohar, A. Graovac, S. Klavžar and J. Žerovnik, Fast computation of the Wiener index of fasciagraphs and rotagraphs, J. Chem. Inf. Comput. Sci. 35 (1995) 834-840.
21. M. Juvan, B. Mohar and J. Žerovnik, Distance-related invariants on polygraphs, Discrete Appl. Math. 80 (1997) 57-71.
22. S. Klavžar and N. Seifter, Dominating Cartesian products of cycles, Discrete Appl. Math. 59 (1995) 129-136.
23. S. Klavžar and J. Žerovnik, Algebraic approach to fasciagraphs and rotagraphs, Discrete Appl. Math. 68 (1996) 93-100.
24. J. van Leeuwen, Graph algorithms, in: J. van Leeuwen, ed., Handbook of Theoretical Computer Science, Volume A, Algorithms and Complexity (Elsevier, Am- sterdam, 1990) 525-631.
25. Livingston and Stout, 25th Int. Conf. on Combinatorics, Graph Theory and Computing, Boca Racon, FL, 1994.
26. M. Petkovšek, A. Vesel and J. Žerovnik, Computing the Szeged index of fasciagraphs and rotagraphs using Mathematica, manuscript in preparation.
27. N. Robertson and P.D. Seymour, Graph minors II. Algorithmic aspects of treewidth, J. Algorithms, 7 (1986) 309-322.
28. W.A. Seitz, D.J. Klein and A. Graovac, Transfer matrix methods for regular polymer graphs, in: R.C. Lacher, ed., Studies in Physical and Theoretical Chemistry, vol. 54 (Elsevier, Amsterdam, 1988) 157-171.
29. J.A. Telle, Complexity of domination-type problems in graphs, Nordic Journal of Computing 1 (1994) 157-171.
30. J.A. Telle and A. Proskurowski, Practical algorithms on partial k-trees with an application to domination-like problems, Lecture Notes in Computer Science 709 (1993) 610-621.
31. A. Wongseelashote, Semirings and path spaces, Discrete Math. 26 (1979) 55-78.
32. U. Zimmermann, Linear and Combinatorial Optimization in Ordered Algebraic Structures (Ann. Discrete Math. 10, North Holland, Amsterdam, 1981).
33. H. Wiener, Structural determination of paraffin boiling points. J. Am. Chem. Soc. 69 (1947) 17-20.