Skip to main content
SpringerLink
Log in

It Is All Labeling

  • Chapter
  • First Online:
Graph Theory

Part of the book series: Problem Books in Mathematics ((PBM))

  • 3994 Accesses

Abstract

The spirit of these papers is that the topics should be presented in an historical context with emphasis on unsolved problems/conjectures. My personal background is a mixture of mathematics and computer science, with a year as a National Research Council/National Bureau of Standards postdoctoral fellow working in the Operations Research Division of NBS headed by Alan Goldman. To put this in context, the mathematician asks if a graph is graceful, the computer scientist asks how efficiently one can find a graceful labeling, and the operations researcher asks if it is not graceful, then how close to graceful is it? I believe the latter outlook actually provides a great source of interesting mathematics/computer science questions.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 29.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 39.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 49.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Anstee, R., Ferguson, R., Griggs, J.: Permutations with low discrepancy consecutive k-sums. J. Comb. Theory A 100, 302–321 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  2. Arumugam, S., Froncek, D., Kamitchi, N.: Distance magic graphs—a survey. International Workshop on Graph Labelings 2010, October 22–23, 2010, University of Wisconsin - Superior

    Google Scholar 

  3. Bange, D.W., Barkauskas, A.E., Slater, P.J.: Simply sequential and graceful graphs. Cong. Num. 23, 155–162 (1979)

    MathSciNet  MATH  Google Scholar 

  4. Bange, D.W., Barkauskas, A.E., Slater, P.J.: Sequentially additive graphs. Discrete Math. 44, 235–241 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  5. Beena, S.: On ∑ and ∑’ labeled graphs. Discrete Math. 309, 1783–1787 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  6. Bascunan, M.E., Ruiz, S., Slater, P.J.: The additive bandwidth of grids and complete bipartite graphs. Cong. Num. 88, 245–254 (1992)

    MathSciNet  MATH  Google Scholar 

  7. Bascunan, M.E., Brigham, R.C., Caron, R.M., Ruiz, S., Slater, P.J., Vitray, R.P.: On the additive bandwidth of graphs. J. Comb. Math. Comb. Comput. 18, 129–144 (1995)

    MathSciNet  MATH  Google Scholar 

  8. Bermond, J.C., Brouwer, A.E., Germa, A.: Systemes de triples et differences associees. In: Colloque CNRS, Problemes Combinatoires et Theorie des Graphes, Orsay, 1976, CNRS, pp. 35–38 (1978)

    Google Scholar 

  9. Bermond, J.C., Kotzig, A., Turgeon, J.: On a combinatorial problem of antennas in radio-astronomy. In: Colloq. Math. Soc. Janos Bolyai 18, Combinatorics, Keszthely, Hungary, 1976, pp. 135–149. North Holland, Amsterdam (1978)

    Google Scholar 

  10. Biraud, F., Blum, E.J., Ribes, J.C.: On optimum synthetic linear arrays. IEEE Trans. Antennas Propag. AP22, 108–109 (1974)

    Article  Google Scholar 

  11. Biraud, F., Blum, E.J., Ribes, J.C.: Some new possibilities of optimum synthetic linear arrays for radio-astronomy. Astron. Astrophys. 41, 409–413 (1975)

    Google Scholar 

  12. Bloom, G.S.: A chronology of the Ringel-Kotzig conjecture and the continuing quest to call all trees graceful. In: Harary, F. (ed.) Topics in Graph Theory (Scientist in Residence Program, New York), pp. 32–51. Academy of Science, Washington (1977)

    Google Scholar 

  13. Browkin, J.: Solution of a certain problem of A. Schinzel. Prace Mat. 3, 205–207 (1959)

    MathSciNet  MATH  Google Scholar 

  14. Farber, M.: Domination, independent domination and duality in strongly chordal graphs. Discret. Appl. Math. 7, 115–130 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  15. Frucht, R.: Graceful numberings of wheels and related graphs. In: Gerwitz, A., Quintas, L. (eds.) Second International Conference on Combinatorial Mathematics, pp. 219–229. The New York Academy of Sciences, New York (1979)

    Google Scholar 

  16. Gallian, J.: A dynamic survey of graph labeling. Electron. J. Comb. (2015), #DS6

    Google Scholar 

  17. Gibbs, R.A., Slater, P.J.: Distinct distance sets in graphs. Discret. Math. 93, 155–165 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  18. Godbold, R., Slater, P.J.: All cycles are edge-magic. Bull. Inst. Combin. Appl. 22, 93–97 (1998)

    MathSciNet  MATH  Google Scholar 

  19. Golomb, S.W.: How to number a graph. In: Read, R.C. (ed.) Graph Theory and Computing, pp. 23–37. Academic Press, New York (1972)

    Chapter  Google Scholar 

  20. Grace, T.: New proof techniques for gracefully labeling graphs. Congr. Numer. 39, 433–439 (1983)

    MathSciNet  Google Scholar 

  21. Hoede, C., Kuiper, H.: All wheels are graceful. Utilitas Math. 14, 311, (1978)

    Google Scholar 

  22. Kotzig, A., Rosa, A.: Magic valuations of finite graphs. Can. Math. Bull. 13, 451–461 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  23. Maheo, M., Thuillier, H.: On d-graceful graphs. Ars Combin. 13, 181–192 (1982)

    MathSciNet  MATH  Google Scholar 

  24. Miller, M., Rodger, C., Simanjutak, R.: Distance magic labelings of graphs. Australas. J. Math. 28, 305–315 (2003)

    MathSciNet  MATH  Google Scholar 

  25. O’Neal, F.A.: Neighborhood sum parameters on graphs. Ph. D. Dissertation, The University of Alabama in Huntsville (2011)

    Google Scholar 

  26. O’Neal, F.A., Slater, P.J.: The minimax, maximin and spread values for open neighborhood sums for 2-regular graphs. Cong. Num. 208, 19–32 (2011)

    MathSciNet  MATH  Google Scholar 

  27. O’Neal, F. A., Slater, P.J.: An introduction to distance D magic graphs. J. Indones. Math. Soc., Special edition, 91–107 (2011)

    Google Scholar 

  28. O’Neal, F.A., Slater, P.J.: An introduction to closed/open neighborhood sums: minimax, maximin and spread. Math. Comput. Sci. 5, 69–80 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  29. O’Neal, F.A., Slater, P.J.: Uniqueness of vertex magic constants. SIAM J. Discret. Math. 27, 708–716 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  30. Ringel, G.: Problem 25. In: Theory of Graphs and Its Applications, Proceeding of the Symposium Smolenice 1963, Prague, p. 162 (1964)

    Google Scholar 

  31. Ringel, G., Llado, A.S.: Another tree conjecture. Bull. Inst. Combin. Appl. 18, 83–85 (1996)

    MathSciNet  MATH  Google Scholar 

  32. Rosa, A.: On certain valuations of the vertices of a graph. In: Rosentiehl, P. (ed.) Theory of Graphs, Proceeding of an International Symposium, Rome, 1966, pp. 349–355. Dunod, Paris (1968)

    Google Scholar 

  33. Schneider, A., Slater, P.J.: Minimax neighborhood sums. Cong. Num. 188, 183–190 (2007)

    MathSciNet  MATH  Google Scholar 

  34. Schneider, A., Slater, P.J.: Minimax open and closed neighborhood sums. AKCE Int. J. Graphs Comb. 6, 183–190 (2009)

    MathSciNet  MATH  Google Scholar 

  35. Sierpinski, W.: Elementary theory of numbers. Warsaw, 411–412 (1964)

    Google Scholar 

  36. Simanjutak, R.: Distance magic labelings and antimagic coverings of graphs, International Workshop on Graph Labelings 2010, October 22–23, 2010, University of Wisconsin - Superior

    Google Scholar 

  37. Slater, P.J.: On k-sequential and other numbered graphs. Discret. Math. 34, 185–193 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  38. Slater, P.J.: On k-graceful graphs. Cong. Num. 36, 53–57 (1982)

    MathSciNet  MATH  Google Scholar 

  39. Slater, P.J.: On repeated difference sequences of a permutation of N. J. Number Theory 16, 1–5 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  40. Slater, P.J.: On k-graceful, locally finite graphs. J. Comb. Theory B 35, 319–322 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  41. Slater, P.J.: Graceful and sequential numberings of infinite graphs. S.E. Asian Bull. Math. 9, 15–22 (1985)

    MathSciNet  MATH  Google Scholar 

  42. Slater, P.J.: On k-graceful countably infinite graphs. Discret. Math. 61, 293–303 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  43. Slater, P.J.: LP-duality, complementarity and generality of graphical subset problems. In: Haynes, T.W., Hedetniemi, S.T., Slater, P.J. (eds.) Domination in Graphs Advanced Topics, pp. 1–30. Marcel Dekker, New York (1998)

    Google Scholar 

  44. Slater, P. J.: How provably graceful are the trees? J. Indones. Math. Soc. 2011, Special edition, 133–135

    Google Scholar 

  45. Slater, P.J., Velez, W.Y.: Permutations of the positive integers with restrictions on the sequence of differences. Pac. J. Math. 71, 193–196 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  46. Slater, P.J., Velez, W.Y.: Permutations of the positive integers with restrictions on the sequence of differences II. Pac. J. Math. 82, 527–531 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  47. Sugeng, K.A., Froncek, D., Miller, M., Ryan, J., Walker, J.: On distance magic labelings of graphs. J. Comb. Math. Comb. Comp. 7, 39–48 (2009)

    MathSciNet  MATH  Google Scholar 

  48. Vilfred, V.: Sigma labeled graphs and circulant graphs. Ph. D. Dissertation, University of Kerala, India (1994)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Science Department, University of Alabama in Huntsville, Huntsville, AL, 35899, USA

    Peter J. Slater

  2. Mathematical Sciences Department, University of Alabama in Huntsville, Huntsville, AL, 35899, USA

    Peter J. Slater

Authors
  1. Peter J. Slater
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Applied Mathematics, Naval Postgraduate School, Monterey, California, USA

    Ralucca Gera

  2. School of Computing, Clemson University, Clemson, South Carolina, USA

    Stephen Hedetniemi

  3. Department of Mathematics, Virginia Commonwealth University, Richmond, Virginia, USA

    Craig Larson

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Slater, P.J. (2016). It Is All Labeling. In: Gera, R., Hedetniemi, S., Larson, C. (eds) Graph Theory. Problem Books in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-31940-7_14

Download citation

Publish with us

Policies and ethics

Search

Navigation