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Article

Keywords:
magic graphs; supermagic graphs; line graphs
Summary:
A graph is called magic (supermagic) if it admits a labelling of the edges by pairwise different (consecutive) positive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. We characterize magic line graphs of general graphs and describe some class of supermagic line graphs of bipartite graphs.
References:
[1] M. Bača, I. Holländer, Ko-Wei Lih: Two classes of super-magic graphs. J. Combin. Math. Combin. Comput. 23 (1997), 113–120. MR 1432751
[2] M. Doob: Characterizations of regular magic graphs. J. Combin. Theory, Ser. B 25 (1978), 94–104. DOI 10.1016/S0095-8956(78)80013-6 | MR 0505855 | Zbl 0384.05054
[3] N. Hartsfield, G. Ringel: Pearls in Graph Theory. Academic Press, San Diego, 1990. MR 1069559
[4] J. Ivančo: On supermagic regular graphs. Math. Bohem. 125 (2000), 99–114. MR 1752082
[5] R. H. Jeurissen: Magic graphs, a characterization. Europ. J. Combin. 9 (1988), 363–368. DOI 10.1016/S0195-6698(88)80066-0 | MR 0950055 | Zbl 0657.05065
[6] S. Jezný, M. Trenkler: Characterization of magic graphs. Czechoslovak Math. J. 33 (1988), 435–438. MR 0718926
[7] J. Sedláček: On magic graphs. Math. Slovaca 26 (1976), 329–335. MR 0434889
[8] J. Sedláček: Problem 27. Theory of Graphs and Its Applications, Proc. Symp. Smolenice. Praha, (1963), 163–164.
[9] B. M. Stewart: Magic graphs. Canad. J. Math. 18 (1966), 1031–1059. MR 0197358 | Zbl 0149.21401
[10] B. M. Stewart: Supermagic complete graphs. Canad. J. Math. 19 (1967), 427–438. DOI 10.4153/CJM-1967-035-9 | MR 0209180 | Zbl 0162.27801
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