Geodesic
Supermagic Graphs with Many Different Degrees
Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 4, pp. 1041-1050.

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Let G = (V, E) be a graph with n vertices and e edges. A supermagic labeling of G is a bijection f from the set of edges E to a set of consecutive integers a, a + 1, . . ., a + e − 1 such that for every vertex v ∈ V the sum of labels of all adjacent edges equals the same constant k. This k is called a magic constant of f, and G is a supermagic graph. The existence of supermagic labeling for certain classes of graphs has been the scope of many papers. For a comprehensive overview see Gallian’s Dynamic survey of graph labeling in the Electronic Journal of Combinatorics. So far, regular or almost regular graphs have been studied. This is natural, since the same magic constant has to be achieved both at vertices of high degree as well as at vertices of low degree, while the labels are distinct consecutive integers.
Keywords: graph labeling, supermagic labeling, non-regular graphs 
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Kovář, Petr; Kravčenko, Michal; Silber, Adam; Krbeček, Matěj. Supermagic Graphs with Many Different Degrees. Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 4, pp. 1041-1050. http://geodesic.mathdoc.fr/item/DMGT_2021_41_4_a10/

[1] M. Bača, I. Holländer and K.-W. Lih, Two classes of super-magic graphs, J. Combin. Math. Combin. Comput. 23 (1997) 113–120.

[2] S. Drajnová, J. Ivančo and A. Semaničová, Numbers of edges in supermagic graphs, J. Graph Theory 52 (2006) 15–26. https://doi.org/10.1002/jgt.20144

[3] J.A. Gallian, A dynamic survey of graph labeling, Electron. J. Combin. (2018) #DS 6.

[4] Y.S. Ho and S.M. Lee, Some initial results on the supermagicness of regular complete k-partite graphs, J. Combin. Math. Combin. Comput. 39 (2001) 3–17.

[5] N. Hartsfield and G. Ringel, Supermagic and antimagic graphs, J. Recreat. Math. 21 (1989) 107–115.

[6] N. Hartsfield and G. Ringel, Pearls in Graph Theory: A Comprehensive Introduction (Academic Press, San Diego, 1990).

[7] J. Ivančo, On supermagic regular graphs, Math. Bohem. 125 (2000) 99–114. https://doi.org/10.21136/MB.2000.126259

[8] J. Ivančo, Z. Lastivková and A. Semaničová, On magic and supermagic line graphs, Math. Bohem. 129 (2004) 33–42. https://doi.org/10.21136/MB.2004.134107

[9] J. Ivančo and T. Polláková, Supermagic graphs having a saturated vertex, Discuss. Math. Graph Theory 34 (2014) 75–84. https://doi.org/10.7151/dmgt.1711

[10] J. Ivančo and A. Semaničová, Some constructions of supermagic graphs using antimagic graphs, SUT J. Math. 42 (2006) 177–186.

[11] J. Ivančo and A. Semaničová, Some constructions of supermagic non-regular graphs, Australas. J. Combin. 38 (2007) 127–139.

[12] J. Sedláček, On magic graphs, Math. Slovaca 26 (1976) 329–335.

[13] J. Sedláček, Problem 27, in: Theory of Graphs and Its Applications, (Proc. Symp. Smolenice, 1963) 163–164.

[14] W.C. Shiu, P.C.B. Lam and H.L. Cheng, Supermagic labeling of an s-duplicate of K n,n, Congr. Numer. 146 (2000) 119–124.

[15] W.C. Shiu, P.C.B. Lam and S.M. Lee, On a construction of supermagic graphs, J. Combin. Math. Combin. Comput. 42 (2002) 147–160.

[16] B.M. Stewart, Magic graphs, Canad. J. Math. 18 (1966) 1031–1059. https://doi.org/10.4153/CJM-1966-104-7

[17] B.M. Stewart, Supermagic complete graphs, Canad. J. Math. 19 (1967) 427–438. https://doi.org/10.4153/CJM-1967-035-9