Vertex-antimagic total labelings of graphs

• Autorzy: Martin Bača , James A. MacDougall , François Bertault , Mirka Miller , Rinovia Simanjuntak , Slamin
• Języki publikacji: EN

Abstrakty

EN

Open problem 1. For the paths Pₙ and the cycles Cₙ, determine if there is a vertex-antimagic total labeling for every feasible pair (a,d).
Open problem 2. Apart from duality, how can a vertex-antimagic total labeling for a graph be used to construct another vertex-antimagic total labeling for the same graph, preferably with different a and d?
Open problem 3. In Theorem 3, we found a way to construct VATL for a graph G from a vertex-magic total labeling of G. Are there other ways to do this?
Open problem 4. Find, if possible, some structural characteristics of a graph which make a vertex-antimagic total labeling impossible

Słowa kluczowe

EN

super-magic labeling; (a,d)-vertex-antimagic total labeling; (a,d)-antimagic labeling

Kategorie tematyczne

• 05C05: Trees
• 05C38: Paths and cycles
• 05C78: Graph labelling (graceful graphs, bandwidth, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2003
• Tom: 23
• Numer: 1
• Strony: 67-83

Daty

wydano

2003

otrzymano

2001-06-15

poprawiono

2001-10-20

Twórcy

autor

Martin Bača

• Department of Applied Mathematics, Technical University, 04200 Košice, Slovak Republic

autor

James A. MacDougall

• Department of Mathematics, University of Newcastle, NSW 2308, Australia

autor

François Bertault

• Department of Computer Science and Software Engineering, University of Newcastle, NSW 2308, Australia

autor

Mirka Miller

• Department of Computer Science and Software Engineering, University of Newcastle, NSW 2308, Australia

autor

Rinovia Simanjuntak

• Department of Computer Science and Software Engineering, University of Newcastle, NSW 2308, Australia

autor

Slamin

• Department of Computer Science and Software Engineering, University of Newcastle, NSW 2308, Australia

Bibliografia

• [1] M. Bača, I. Holländer and Ko-Wei Lih, Two classes of super-magic quartic graphs, JCMCC 13 (1997) 113-120.
• [2] M. Bača and I. Holländer, On (a,d)-antimagic prisms, Ars. Combin. 48 (1998) 297-306.
• [3] R. Bodendiek and G. Walther, Arithmetisch antimagische graphen, in: K. Wagner and R. Bodendiek, Graphentheorie III, (BI-Wiss. Verl., Mannheim-Leipzig-Wien-Zürich, 1993).
• [4] M. Doob, Generalizations of magic graphs, J. Combin. Theory (B) 17 (1974) 205-217, doi: 10.1016/0095-8956(74)90027-6.
• [5] J.A. Gallian, A dynamic survey of graph labeling, Electronic. J. Combin. 5 (1998) #DS6.
• [6] N. Hartsfield and G. Ringel, Pearls in Graph Theory (Academic Press, Boston-San Diego-New York-London, 1990).
• [7] R.H. Jeurissen, Magic graphs, a characterization, Report 8201 (Mathematisch Instituut, Katholieke Universiteit Nijmegen, 1982).
• [8] S. Jezný and M. Trenkler, Charaterization of magic graphs, Czechoslovak Math. J. 33 (1983) 435-438.
• [9] A. Kotzig and A. Rosa, Magic valuations of finite graphs, Canad. Math. Bull. 13 (1970) 451-461, doi: 10.4153/CMB-1970-084-1.
• [10] J.A. MacDougall, M. Miller, Slamin, and W.D. Wallis, Vertex-magic total labelings of graphs, Utilitas Math., to appear.
• [11] M. Miller and M. Bača, Antimagic valuations of generalized Petersen graphs, Australasian J. Combin. 22 (2000) 135-139.
• [12] J. Sedlácek, Problem 27 in Theory of Graphs and its Applications, Proc. Symp. Smolenice, June 1963, Praha (1964), p. 162.
• [13] B.M. Stewart, Supermagic complete graphs, Can. J. Math. 19 (1967) 427-438, doi: 10.4153/CJM-1967-035-9.
• [14] W.D. Wallis, E.T. Baskoro, M. Miller and Slamin, Edge-magic total labelings of graphs, Australasian J. Combin. 22 (2000) 177-190.
• [15] D.B. West, An Introduction to Graph Theory (Prentice-Hall, 1996).

Identyfikatory

DOI

10.7151/dmgt.1186