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2000 | 20 | 2 | 219-229
Tytuł artykułu

Survey of certain valuations of graphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The study of valuations of graphs is a relatively young part of graph theory. In this article we survey what is known about certain graph valuations, that is, labeling methods: antimagic labelings, edge-magic total labelings and vertex-magic total labelings.
Wydawca
Rocznik
Tom
20
Numer
2
Strony
219-229
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-11-22
poprawiono
2000-10-18
Twórcy
autor
  • Department of Applied Mathematics, Technical University, Košice 042 00, Slovakia
  • Department of Mathematics, The University of Newcastle, NSW 2308, Australia
autor
  • Department of Computer Science and Software Engineering, The University of Newcastle, NSW 2308, Australia
autor
  • Department of Mathematical Education, Universitas Jember, Jember 68121, Indonesia
autor
  • Department of Mathematics, Southern Illinois University, Carbondale, IL 62901-4408, USA
Bibliografia
  • [1] M. Bača and I. Holländer, On (a,d)-antimagic prisms, Ars Combinatoria 48 (1998) 297-306.
  • [2] M. Bača, Antimagic labelings of antiprisms, JCMCC, to appear.
  • [3] M. Bača, Special face numbering of plane quartic graphs, Ars Combinatoria, to appear.
  • [4] M. Bača, Face-antimagic labelings of convex polytopes, Utilitas Math. 55 (1999) 221-226.
  • [5] M. Bača, Consecutive-magic labeling of generalized Petersen graphs, Utilitas Math., to appear.
  • [6] M. Bača and Mirka Miller, Antimagic face labeling of convex polytopes based on biprisms, JCMCC, to appear.
  • [7] G.S. Bloom, A chronology of the Ringel-Kotzig conjecture and the continuing quest to call all trees graceful, Ann. N.Y. Acad. Sci. 326 (1979) 32-51, doi: 10.1111/j.1749-6632.1979.tb17766.x.
  • [8] G.S. Bloom and S.W. Golomb, Applications of numbered undirected graphs, Proc. IEEE 65 (1977) 562-570, doi: 10.1109/PROC.1977.10517.
  • [9] R. Bodendiek and G. Walther, Arithmetisch antimagische graphen, in: K. Wagner and R. Bodendiek, eds., Graphentheorie III (BI-Wiss.Verl., Mannheim, 1993).
  • [10] R. Bodendiek and G. Walther, On number theoretical methods in graph labelings, Res. Exp. Math. 21 (1995) 3-25.
  • [11] R. Bodendiek and G. Walther, On (a,d)-antimagic parachutes, Ars Combinatoria 42 (1996) 129-149.
  • [12] R. Bodendiek and G. Walther, On (a,d)-antimagic parachutes II, Ars Combinatoria 46 (1997) 33-63.
  • [13] M. Borowiecki and L.V. Quintas, Magic digraphs, in: 33. Intern. Wiss. Koll. TH Ilmenau (1988) 163-166.
  • [14] H. Enomoto, A.S. Llado, T. Nakamigawa and G. Ringel, Super edge-magic graphs, SUT J. Math. 2 (1998) 105-109.
  • [15] R. Frucht and J.A. Gallian, Labeling prisms, Ars Combinatoria 26 (1988) 69-82.
  • [16] J.A. Gallian, A dynamic survey of graph labeling, Electronic J. Combinatorics 5 (1998) #DS6.
  • [17] N. Hartsfield and G Ringel, Pearls in Graph Theory (Academic Press, 1990).
  • [18] R.H. Jeurissen, Magic graphs, a characterization, Report 8201, Mathematisch Instituut, Katholieke Universiteit Nijmegen, 1982.
  • [19] S. Jezný and M. Trenkler, Characterization of magic graphs, Czechoslovak Math. J. 33 (1983) 435-438.
  • [20] A. Kotzig and A. Rosa, Magic valuations of finite graphs, Canad. Math. Bull. 13 (1970) 451-461, doi: 10.4153/CMB-1970-084-1.
  • [21] A. Kotzig and A. Rosa, Magic valuations of complete graphs, Publ. CRM 175 (1972).
  • [22] J.A. MacDougall, Mirka Miller, Slamin and W.D. Wallis, Vertex-magic total labellings of graphs, submitted.
  • [23] Mirka Miller, J.A. MacDougall, Slamin and W.D. Wallis, Problems in magic total graph labellings, in: Proceedings of the tenth AWOCA (1999) 19-25.
  • [24] Mirka Miller and M. Bača, Antimagic valuations of generalized Petersen graphs, Australasian J. Combin. 22 (2000) 135-139.
  • [25] Mirka Miller, M. Bača and Y. Lin, On two conjectures concerning (a,d)-antimagic labellings of antiprisms, JCMCC, to appear.
  • [26] Mirka Miller, M. Bača and J. A. MacDougall, Vertex-magic total labeling of the generalized Petersen graphs and convex polytopes, submitted.
  • [27] G. Ringel, Problem 25, Theory of Graphs and its Applications, in: Proc. Symposium Smolenice 1963 (Prague, 1964) 162.
  • [28] G. Ringel and A.S. Llado, Another tree conjecture, Bull. ICA 18 (1996) 83-85.
  • [29] A. Rosa, On certain valuations of the vertices of a graph, in: Theory of Graphs (Internat. Symposium, Rome, July 1966; Gordon and Breach, N.Y. and Dunod Paris, 1967) 349-355.
  • [30] J. Sedlácek, Problem 27, in: Theory of Graphs and its Applications, Proc. Symposium Smolenice 1963 (Prague, 1964) 163-164.
  • [31] B.M. Stewart, Supermagic complete graphs, Canad. J. Math. 19 (1967) 427-438, doi: 10.4153/CJM-1967-035-9.
  • [32] W.D. Wallis, E.T. Baskoro, Mirka Miller and Slamin, Edge-magic total labelings, submitted.
  • [33] M.E. Watkins, A theorem on Tait colorings with an application to the generalized Petersen graphs, J. Combin. Theory 6 (1969) 152-164, doi: 10.1016/S0021-9800(69)80116-X.
  • [34] D.B. West, An Introduction to Graph Theory (Prentice-Hall, 1996).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1121
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