# Supermagic Graphs Having a Saturated Vertex

Jaroslav Ivančo; Tatiana Polláková

Discussiones Mathematicae Graph Theory (2014)

- Volume: 34, Issue: 1, page 75-84
- ISSN: 2083-5892

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topJaroslav Ivančo, and Tatiana Polláková. "Supermagic Graphs Having a Saturated Vertex." Discussiones Mathematicae Graph Theory 34.1 (2014): 75-84. <http://eudml.org/doc/267718>.

@article{JaroslavIvančo2014,

abstract = {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.},

author = {Jaroslav Ivančo, Tatiana Polláková},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {supermagic graph; saturated vertex; vertex-magic total labeling},

language = {eng},

number = {1},

pages = {75-84},

title = {Supermagic Graphs Having a Saturated Vertex},

url = {http://eudml.org/doc/267718},

volume = {34},

year = {2014},

}

TY - JOUR

AU - Jaroslav Ivančo

AU - Tatiana Polláková

TI - Supermagic Graphs Having a Saturated Vertex

JO - Discussiones Mathematicae Graph Theory

PY - 2014

VL - 34

IS - 1

SP - 75

EP - 84

AB - 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.

LA - eng

KW - supermagic graph; saturated vertex; vertex-magic total labeling

UR - http://eudml.org/doc/267718

ER -

## References

top- [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] Zbl1238.05226
- [2] J.A. Gallian, A dynamic survey of graph labeling, Electron. J. Combin. 18 (2011) #DS6. Zbl0953.05067
- [3] J. Ivančo, On supermagic regular graphs, Math. Bohem. 125 (2000) 99-114. Zbl0963.05121
- [4] J. Ivančo, Magic and supermagic dense bipartite graphs, Discuss. Math. Graph Theory 27 (2007) 583-591. doi:10.7151/dmgt.1384[Crossref] Zbl1142.05071
- [5] J. Ivančo, A construction of supermagic graphs, AKCE Int. J. Graphs Comb. 6 (2009) 91-102. Zbl1210.05145
- [6] J. Ivančo and T. Polláková, On magic joins of graphs, Math. Bohem. (to appear). Zbl1274.05420
- [7] J. Ivančo and A. Semaničová, Some constructions of supermagic graphs using antimagic graphs, SUT J. Math. 42 (2006) 177-186. Zbl1136.05065
- [8] J.A. MacDougall, M. Miller, Slamin and W.D. Wallis, Vertex-magic total labelings of graphs, Util. Math. 61 (2002) 3-21. Zbl1008.05135
- [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. Zbl1164.05060
- [11] B.M. Stewart, Magic graphs, Canad. J. Math. 18 (1966) 1031-1059. doi:10.4153/CJM-1966-104-7[Crossref] Zbl0149.21401
- [12] W.D. Wallis, Magic Graphs (Birkhäuser, Boston - Basel - Berlin, 2001). doi:10.1007/978-1-4612-0123-6[Crossref]

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