Skip to main content
Top

2017 | OriginalPaper | Chapter

2. Graphs Labelings

Authors : Susana C. López, Francesc A. Muntaner-Batle

Published in: Graceful, Harmonious and Magic Type Labelings

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

By a labeling of a graph, also known as a valuation of a graph, we mean a map that carries graph elements onto numbers (usually the positive or nonnegative integers) called labels that meet some properties depending on the type of labeling that we are considering. The most common choices for the domain are the set of vertices alone (vertex labelings), or edges alone (edge labelings), or the set of edges and vertices together (total labelings) (see [12]). Other domains are also possible, but they will not be discussed in this book.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Footnotes
1
With permission from [10], ©2001, Elsevier.
 
Literature
2.
go back to reference Bača, M., Miller, M.: Super Edge-Antimagic Graphs. BrownWalker Press, Boca Raton (2008)MATH Bača, M., Miller, M.: Super Edge-Antimagic Graphs. BrownWalker Press, Boca Raton (2008)MATH
3.
go back to reference Bača, M., Baskoro, E.T., Simanjuntak, R., Sugeng, K.A.: Super edge-antimagic labelings of the generalized Petersen graph P(n, (n − 1)∕2). Utilitas Math. 70, 119–127 (2006) Bača, M., Baskoro, E.T., Simanjuntak, R., Sugeng, K.A.: Super edge-antimagic labelings of the generalized Petersen graph P(n, (n − 1)∕2). Utilitas Math. 70, 119–127 (2006)
4.
go back to reference Bodendiek, R., Walther, G.: Arithmetish a timagishe graphen. In: Graphentheorie III. Bi-Weiss Ver., Mannheim (1993) Bodendiek, R., Walther, G.: Arithmetish a timagishe graphen. In: Graphentheorie III. Bi-Weiss Ver., Mannheim (1993)
5.
go back to reference Brankovic, L., Murch, C., Pond, J., Rosa, A.: Alpha-size of trees with maxi- mum degree three and perfect matching. In: Proceedings of AWOCA 2005, pp. 47–56 (2005) Brankovic, L., Murch, C., Pond, J., Rosa, A.: Alpha-size of trees with maxi- mum degree three and perfect matching. In: Proceedings of AWOCA 2005, pp. 47–56 (2005)
6.
go back to reference Cahit, I.: Cordial graphs: a weaker version of graceful and harmonious graphs. Ars Comb. 23, 201–207 (1987)MathSciNetMATH Cahit, I.: Cordial graphs: a weaker version of graceful and harmonious graphs. Ars Comb. 23, 201–207 (1987)MathSciNetMATH
7.
go back to reference Chang, G.J., Hsu, D.F., Rogers, D.G.: Additive variations on a graceful theme: some results on harmonious and other related graphs. Congr. Numer. 32, 181–197 (1981)MathSciNetMATH Chang, G.J., Hsu, D.F., Rogers, D.G.: Additive variations on a graceful theme: some results on harmonious and other related graphs. Congr. Numer. 32, 181–197 (1981)MathSciNetMATH
9.
go back to reference Enomoto, H., Lladó, A., Nakamigawa, T., Ringel, G.: Super edge-magic graphs. SUT J. Math. 34, 105–109 (1998)MathSciNetMATH Enomoto, H., Lladó, A., Nakamigawa, T., Ringel, G.: Super edge-magic graphs. SUT J. Math. 34, 105–109 (1998)MathSciNetMATH
11.
go back to reference Fukuchi, Y.: Edge-magic labelings of generalized Petersen graphs p(n, 2). Ars Comb. 59, 253–257 (2001) Fukuchi, Y.: Edge-magic labelings of generalized Petersen graphs p(n, 2). Ars Comb. 59, 253–257 (2001)
12.
go back to reference Gallian, J.A.: A dynamic survey of graph labeling. Electron. J. Comb. 19 (DS6) (2016) Gallian, J.A.: A dynamic survey of graph labeling. Electron. J. Comb. 19 (DS6) (2016)
13.
go back to reference Golomb, S.W.: How to number a graph. In: Graph Theory and Computing, pp. 23–37. Academic, New York (1972) Golomb, S.W.: How to number a graph. In: Graph Theory and Computing, pp. 23–37. Academic, New York (1972)
14.
go back to reference Grace, T.: On sequencial labelings of graphs. J. Graph Theory 7Ish, 195–201 (1983) Grace, T.: On sequencial labelings of graphs. J. Graph Theory 7Ish, 195–201 (1983)
15.
17.
go back to reference Ichishima, R., Oshima, A.: On the super edge-magic deficiency and α-valuations of graphs. Ars Comb. 129, 157–163 (2016) Ichishima, R., Oshima, A.: On the super edge-magic deficiency and α-valuations of graphs. Ars Comb. 129, 157–163 (2016)
18.
go back to reference Kotzig, A.: On a class of graphs without magic valuations. Reports of the CRM CRM-136 (1971) Kotzig, A.: On a class of graphs without magic valuations. Reports of the CRM CRM-136 (1971)
19.
go back to reference Kotzig, A.: β-valuations of quadratic graphs with isomorphic components. Utilitas Math. 7, 263–279 (1975) Kotzig, A.: β-valuations of quadratic graphs with isomorphic components. Utilitas Math. 7, 263–279 (1975)
20.
go back to reference Kotzig, A.: Recent results and open problems in graceful graphs. Congr. Numer. 44, 197–219 (1984)MathSciNetMATH Kotzig, A.: Recent results and open problems in graceful graphs. Congr. Numer. 44, 197–219 (1984)MathSciNetMATH
22.
go back to reference Kotzig, A., Rosa, A.: Magic valuations of complete graphs. Publ. CRM 175 (1972) Kotzig, A., Rosa, A.: Magic valuations of complete graphs. Publ. CRM 175 (1972)
23.
go back to reference MacDougall, J.A., Miller, M., Slamin, Wallis, W.D.: Vertex-magic total labelings of graphs. Utilitas Math. 61, 3–21 (2002) MacDougall, J.A., Miller, M., Slamin, Wallis, W.D.: Vertex-magic total labelings of graphs. Utilitas Math. 61, 3–21 (2002)
25.
go back to reference Muntaner-Batle, F.A.: Special super edge-magic labelings of bipartite graphs. J. Comb. Math. Comb. Comput. 39, 107–120 (2001)MathSciNetMATH Muntaner-Batle, F.A.: Special super edge-magic labelings of bipartite graphs. J. Comb. Math. Comb. Comput. 39, 107–120 (2001)MathSciNetMATH
27.
go back to reference Redd, T.: Graceful graphs and graceful labelings: two mathematical formulations and some other new results. Congr. Numer. 164, 17–31 (2003)MathSciNetMATH Redd, T.: Graceful graphs and graceful labelings: two mathematical formulations and some other new results. Congr. Numer. 164, 17–31 (2003)MathSciNetMATH
28.
go back to reference Ringel, G.: Problem 2.5. In: Theory of Graphs and Its Application (Proc. Sympos. Smolenice 1963), p. 162. Nakl. CSAV, Praha (1964) Ringel, G.: Problem 2.5. In: Theory of Graphs and Its Application (Proc. Sympos. Smolenice 1963), p. 162. Nakl. CSAV, Praha (1964)
29.
30.
31.
go back to reference Rosa, A.: On certain valuations of the vertices of a graph. In: Theory of Graphs (Internat. Symposium, Rome, July 1966), pp. 349–355. Gordon and Breach/Dunod, New York/Paris (1967) Rosa, A.: On certain valuations of the vertices of a graph. In: Theory of Graphs (Internat. Symposium, Rome, July 1966), pp. 349–355. Gordon and Breach/Dunod, New York/Paris (1967)
32.
go back to reference Sedláček, J.: Problem 2.7. In: Theory of Graphs and its Application (Proc. Sympos. Smolenice 1963), pp. 163–164. Nakl. CSAV, Praha (1964) Sedláček, J.: Problem 2.7. In: Theory of Graphs and its Application (Proc. Sympos. Smolenice 1963), pp. 163–164. Nakl. CSAV, Praha (1964)
33.
go back to reference Simanjuntak, R., Bertault, F., Miller, M.: Two new (a, d)-antimagic graph labelings. In: Proc. of Eleventh Australasian Workshop on Combinatorial Algorithms, pp. 149–158 (2000) Simanjuntak, R., Bertault, F., Miller, M.: Two new (a, d)-antimagic graph labelings. In: Proc. of Eleventh Australasian Workshop on Combinatorial Algorithms, pp. 149–158 (2000)
37.
go back to reference Valdés, L.: Edge-magic K p . In: Thirty-Second South-Eastern International Conference on Combinatorics, Graph Theory and Computing, Baton Rouge, LA, vol. 153, pp. 107–111 (2001)MATH Valdés, L.: Edge-magic K p . In: Thirty-Second South-Eastern International Conference on Combinatorics, Graph Theory and Computing, Baton Rouge, LA, vol. 153, pp. 107–111 (2001)MATH
Metadata
Title
Graphs Labelings
Authors
Susana C. López
Francesc A. Muntaner-Batle
Copyright Year
2017
DOI
https://doi.org/10.1007/978-3-319-52657-7_2

Premium Partner