A graph is called supermagic if it admits a labeling of the edges by pairwise different consecutive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In this paper we establish some conditions for graphs with a saturated vertex to be supermagic. Inter alia we show that complete multipartite graphs K1,n,n and K1,2,...,2 are supermagic.
@article{bwmeta1.element.doi-10_7151_dmgt_1711,
author = {Jaroslav Ivan\v co and Tatiana Poll\'akov\'a},
title = {Supermagic Graphs Having a Saturated Vertex},
journal = {Discussiones Mathematicae Graph Theory},
volume = {34},
year = {2014},
pages = {75-84},
zbl = {1292.05224},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1711}
}
Jaroslav Ivančo; Tatiana Polláková. Supermagic Graphs Having a Saturated Vertex. Discussiones Mathematicae Graph Theory, Tome 34 (2014) pp. 75-84. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1711/
[1] L’. Bezegová and J. Ivančo, On conservative and supermagic graphs, Discrete Math. 311 (2011) 2428-2436. doi:10.1016/j.disc.2011.07.014[Crossref] | Zbl 1238.05226
[2] J.A. Gallian, A dynamic survey of graph labeling, Electron. J. Combin. 18 (2011) #DS6. | Zbl 0953.05067
[3] J. Ivančo, On supermagic regular graphs, Math. Bohem. 125 (2000) 99-114. | Zbl 0963.05121
[4] J. Ivančo, Magic and supermagic dense bipartite graphs, Discuss. Math. Graph Theory 27 (2007) 583-591. doi:10.7151/dmgt.1384[Crossref] | Zbl 1142.05071
[5] J. Ivančo, A construction of supermagic graphs, AKCE Int. J. Graphs Comb. 6 (2009) 91-102. | Zbl 1210.05145
[6] J. Ivančo and T. Polláková, On magic joins of graphs, Math. Bohem. (to appear). | Zbl 1274.05420
[7] J. Ivančo and A. Semaničová, Some constructions of supermagic graphs using antimagic graphs, SUT J. Math. 42 (2006) 177-186. | Zbl 1136.05065
[8] J.A. MacDougall, M. Miller, Slamin and W.D. Wallis, Vertex-magic total labelings of graphs, Util. Math. 61 (2002) 3-21. | Zbl 1008.05135
[9] J. Sedláček, Problem 27. Theory of Graphs and Its Applications, Proc. Symp. Smolenice, Praha (1963) 163-164.
[10] A. Semaničová, Magic graphs having a saturated vertex, Tatra Mt. Math. Publ. 36 (2007) 121-128. | Zbl 1164.05060
[11] B.M. Stewart, Magic graphs, Canad. J. Math. 18 (1966) 1031-1059. doi:10.4153/CJM-1966-104-7[Crossref] | Zbl 0149.21401
[12] W.D. Wallis, Magic Graphs (Birkhäuser, Boston - Basel - Berlin, 2001). doi:10.1007/978-1-4612-0123-6[Crossref]