Volume 19, Issue No.3


H-covering, (a,d)-H-antimagic graph, super (a,d)-H-antimagic graph, partition of set.


Let G = (V,E) be a finite simple graph with p vertices and q edges. An edge-covering of G is a family of subgraphs H1,H2,...,Ht such that each edge of E(G) belongs to at least one of the subgraphs Hi, i=1,2,...,t. If every subgraph Hi is isomorphic to a given graph H, then the graph G admits an H-covering. Such a graph G is called (a,d)-H-antimagic if there is a bijection f: VjEg{1,2,...,p+q} such that for all subgraphs H′ of G isomorphic to H, the sum of the labels of all the edges and vertices belonging to H′ constitutes an arithmetic progression with the initial term a and the common difference d. When f(V)={1,2,...,p}, then G is said to be super (a,d)-H-antimagic; and if d = 0 then G is called H-supermagic. We will exhibit an operation on graphs which keeps super H-antimagic properties. We use a technique of partitioning sets of integers for the construction of the
required labelings.


Acta Mechanica Slovaca. Volume 19, Issue 3, Pages 6–11, ISSN 1335-2393


  A Construction of H-antimagic Graphs


[1] Bača, M., Brankovic, L., Semaničová-Feňovčíková, A.: Labelings of plane graphs with determined face weights, Acta Mechanica Slovaca, vol 13(2), 2009, p. 64-71.

[2] Bača, M., Brankovic, L., Semaničová-Feňovčíková, A.: Labelings of plane graphs containing Hamilton path, Acta Math. Sinica - English Series, vol 27(4), 2011, p. 701-714.

[3] Bača, M., Miller, M., Phanalasy, O., Semaničová-Feňovčíková, A., Super d-antimagic labelings of disconnected plane graphs, Acta Math. Sinica - English Series, vol 26(12), 2010, p. 2283-2294.

[4] Bača, M., Lin, Y., Muntaner-Batle, F.A., Rius-Font, M., Strong labelings of linear forests, Acta Math. Sinica - English Series, vol 25(12), 2009, p. 1951-1964.

[5] Bača, M., Miller, M., Super edge-antimagic graphs: A wealth of problems and some solutions, Brown Walker Press, Boca Raton, Florida, 2008.

[6] Bača, M., Numan, M., Shabbir, A., Labelings of type (1,1,1) for toroidal fullerenes, Turkish Journal of Mathematics, vol 37, 2013, p. 899-907.

[7] Enomoto, H., Lladó, A.S., Nakamigawa, T., Ringel, G., Super edge-magic graphs, SUT J. Math., vol 34, 1998, p. 105-109

[8] Figueroa-Centeno, R.M., Ichishima, R., Muntaner-Batle, F.A., The place of super edge-magic labelings among other classes of labelings, Discrete Math., vol 231, 2001, p. 153-168.

[9] Gutiérrez, A., Lladó, A., Magic coverings, J. Combin. Math. Combin. Comput., vol 55, 2005, p. 43-56.

[10] Inayah, N., Salman, A.N.M., Simanjuntak, R., On (a,d)-Hantimagic coverings of graphs, J. Combin. Math. Combin. Comput., vol 71, 2009, p. 273-281.

[11] Inayah, N., Simanjuntak, R., Salman, A.N.M., Syuhada, K.I.A., On (a,d)-H-antimagic total labelings for shackles of a connected graph H, Australasian J. Combin., vol 57, 2013, p.127-138.

[12] Jeyanthi, P., Selvagopal, P., More classes of H-supermagic graphs, Internat. J. Algor. Comput. Math., vol 3, 2010, 93-108.

[13] Kotzig, A., Rosa, A., Magic valuations of finite graphs, Canad. Math. Bull., vol 13, 1970, p. 451-461.

[14] Lih, K.W., On magic and consecutive labelings of plane graphs, Utilitas Math., vol 24, 1983, p. 165-197.

[15] Lladó, A., Moragas, J., Cycle-magic graphs, Discrete Math., vol 307, 2007, p. 2925-2933.

[16] Marr, A.M., Wallis, W.D., Magic Graphs, Birkhäuser, New York, 2013.

[17] Maryati, T.K., Baskoro, E.T., Salman, A.N.M., Ph-(super)magic labelings of some trees, J. Combin. Math. Combin. Comput., vol 65, 2008, p. 198-204.

[18] Maryati, T.K., Salman, A.N.M., Baskoro, E.T., Supermagic coverings of the disjoint union of graphs and amalgamations, Discrete Math., vol. 313, 2013, p. 397-405.

[19] Ngurah, A.A.G., Salman, A.N.M., Susilowati, L., H-supermagic labelings of graphs, Discrete Math., vol 310, 2010, p. 1293-1300.

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