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

Abstract

top
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.

How to cite

top

Jaroslav 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. [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. [2] J.A. Gallian, A dynamic survey of graph labeling, Electron. J. Combin. 18 (2011) #DS6. Zbl0953.05067
  3. [3] J. Ivančo, On supermagic regular graphs, Math. Bohem. 125 (2000) 99-114. Zbl0963.05121
  4. [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. [5] J. Ivančo, A construction of supermagic graphs, AKCE Int. J. Graphs Comb. 6 (2009) 91-102. Zbl1210.05145
  6. [6] J. Ivančo and T. Polláková, On magic joins of graphs, Math. Bohem. (to appear). Zbl1274.05420
  7. [7] J. Ivančo and A. Semaničová, Some constructions of supermagic graphs using antimagic graphs, SUT J. Math. 42 (2006) 177-186. Zbl1136.05065
  8. [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. [9] J. Sedláček, Problem 27. Theory of Graphs and Its Applications, Proc. Symp. Smolenice, Praha (1963) 163-164. 
  10. [10] A. Semaničová, Magic graphs having a saturated vertex, Tatra Mt. Math. Publ. 36 (2007) 121-128. Zbl1164.05060
  11. [11] B.M. Stewart, Magic graphs, Canad. J. Math. 18 (1966) 1031-1059. doi:10.4153/CJM-1966-104-7[Crossref] Zbl0149.21401
  12. [12] W.D. Wallis, Magic Graphs (Birkhäuser, Boston - Basel - Berlin, 2001). doi:10.1007/978-1-4612-0123-6[Crossref] 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.