Geodesic
Union of Distance Magic Graphs
Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 1, pp. 239-249.

Voir la notice de l'article provenant de la source Library of Science

A distance magic labeling of a graph G = (V,E) with |V | = n is a bijection 𝓁 from V to the set 1, . . ., n such that the weight w(x) = Σ_ y ∈ N_G (x) 𝓁(y) of every vertex x ∈ V is equal to the same element μ, called the magic constant. In this paper, we study unions of distance magic graphs as well as some properties of such graphs.
Keywords: distance magic labeling, magic constant, sigma labeling, graph labeling, union of graphs, lexicographic product, direct product, Kronecker product, Kotzig array 
@article{DMGT_2017_37_1_a16,
     author = {Cichacz, Sylwia and Nikodem, Mateusz},
     title = {Union of {Distance} {Magic} {Graphs}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {239--249},
     publisher = {mathdoc},
     volume = {37},
     number = {1},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2017_37_1_a16/}
}
TY  - JOUR
AU  - Cichacz, Sylwia
AU  - Nikodem, Mateusz
TI  - Union of Distance Magic Graphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2017
SP  - 239
EP  - 249
VL  - 37
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2017_37_1_a16/
LA  - en
ID  - DMGT_2017_37_1_a16
ER  - 
%0 Journal Article
%A Cichacz, Sylwia
%A Nikodem, Mateusz
%T Union of Distance Magic Graphs
%J Discussiones Mathematicae. Graph Theory
%D 2017
%P 239-249
%V 37
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2017_37_1_a16/
%G en
%F DMGT_2017_37_1_a16
Cichacz, Sylwia; Nikodem, Mateusz. Union of Distance Magic Graphs. Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 1, pp. 239-249. http://geodesic.mathdoc.fr/item/DMGT_2017_37_1_a16/

[1] M. Anholcer and S. Cichacz, Note on distance magic products G ○ C4, Graphs Combin. 31 (2015) 1117–1124. doi:10.1007/s00373-014-1453-x

[2] M. Anholcer, S. Cichacz, I. Peterin and A. Tepeh, Distance magic labeling and two products of graphs, Graphs Combin. 31 (2015) 1125–1136. doi:10.1007/s00373-014-1455-8

[3] M. Anholcer, S. Cichacz and I. Peterin, Spectra of graphs and closed distance magic labelings, (2014) preprint.

[4] S. Beena, On ∑ and ∑′ labelled graphs, Discrete Math. 309 (2009) 1783–1787. doi:10.1016/j.disc.2008.02.038

[5] S. Cichacz, Group distance magic graphs G × Cn, Discrete Appl. Math. 177 (2014) 80–87. doi:10.1016/j.dam.2014.05.044

[6] S. Cichacz, Distance magic (r, t)-hypercycles, Util. Math. 101 (2016) 283–294.

[7] S. Cichacz and D. Froncek, Distance magic circulant graphs, Discrete Math. 339 (2016) 84–94.

[8] S. Cichacz, D. Froncek, E. Krop and C. Raridan, Distance magic Cartesian product of two graphs, Discuss. Math. Graph Theory 36 (2016) 299–308. doi:10.7151/dmgt.1852

[9] S. Cichacz and A. Görlich Constant sum partition of set of integers and distance magic graphs, (2013) preprint.

[10] R. Diestel, Graph Theory, Third Edition (Springer-Verlag, Heidelberg Graduate Texts in Mathematics, Volume 173, New York, 2005).

[11] D. Froncek, Handicap distance antimagic graphs and incomplete tournaments, AKCE Int. J. Graphs Comb. 10 (2013) 119–127.

[12] D. Froncek, P. Kovář and T. Kovářová, Fair incomplete tournaments, Bull. Inst. Combin. Appl. 48 (2006) 31–33.

[13] D. Froncek, P. Kovář and T. Kovářová, Constructing distance magic graphs from regular graphs, J. Combin. Math. Combin. Comput. 78 (2011) 349–354.

[14] J.A. Gallian, A dynamic survey of graph labeling, Electron. J. Combin. DS6. http://www.combinatorics.org/Surveys/

[15] P. Gregor and P. Kovář, Distance magic labelings of hypercubes, Electron. Notes Discrete Math. 40 (2013) 145–149. doi:10.1016/j.endm.2013.05.027

[16] R. Hammack, W. Imrich and S. Klavžar, Handbook of Product Graphs, Second Edition (CRC Press, Boca Raton, FL, 2011).

[17] F. Harary, Graph Theory (Addison-Wesley, 1994).

[18] P.K. Jha, S. Klažar and B. Zmazek, Isomorphic components of Kronecker product of bipartite graphs, Preprint Ser. Univ. Ljubljana 32 (1994) no. 452.

[19] R.H. Lamprey and B.H. Barnes, Product graphs and their applications, in: Proc. Fifth Annual Pittsburgh Conference, Instrument Society of America, Pittsburgh, PA, 1974, Modelling and Simulation 5 (1974) 1119–1123.

[20] M.K. Shafiq, G. Ali and R. Simanjuntak, Distance magic labelings of a union of graphs, AKCE Int. J. Graphs. Combin. 6 (2009) 191–200.

[21] M. Miller, C. Rodger and R. Simanjuntak, Distance magic labelings of graphs, Australas. J. Combin. 28 (2003) 305–315.

[22] S.B. Rao, T. Singh and V. Parameswaran, Some sigma labelled graphs I, in: Graphs, Combinatorics, Algorithms and Applications, S. Arumugam, B.D. Acharya and S.B. Rao (Ed(s)), (Narosa Publishing House, New Delhi, 2004) 125–133.

[23] W.D. Wallis, Vertex magic labelings of multiple graphs, Congr. Numer. 152 (2001) 81–83.