Geodesic
A Note on Neighbor Expanded Sum Distinguishing Index
Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 1, pp. 29-37.

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

A total k-coloring of a graph G is a coloring of vertices and edges of G using colors of the set [k] = 1, . . ., k. These colors can be used to distinguish the vertices of G. There are many possibilities of such a distinction. In this paper, we consider the sum of colors on incident edges and adjacent vertices.
Keywords: general edge coloring, total coloring, neighbor-distinguishing index, neighbor sum distinguishing coloring 
@article{DMGT_2017_37_1_a2,
     author = {Flandrin, Evelyne and Li, Hao and Marczyk, Antoni and Sacl\'e, Jean-Fran\c{c}ois and Wo\'zniak, Mariusz},
     title = {A {Note} on {Neighbor} {Expanded} {Sum} {Distinguishing} {Index}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {29--37},
     publisher = {mathdoc},
     volume = {37},
     number = {1},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2017_37_1_a2/}
}
TY  - JOUR
AU  - Flandrin, Evelyne
AU  - Li, Hao
AU  - Marczyk, Antoni
AU  - Saclé, Jean-François
AU  - Woźniak, Mariusz
TI  - A Note on Neighbor Expanded Sum Distinguishing Index
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2017
SP  - 29
EP  - 37
VL  - 37
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2017_37_1_a2/
LA  - en
ID  - DMGT_2017_37_1_a2
ER  - 
%0 Journal Article
%A Flandrin, Evelyne
%A Li, Hao
%A Marczyk, Antoni
%A Saclé, Jean-François
%A Woźniak, Mariusz
%T A Note on Neighbor Expanded Sum Distinguishing Index
%J Discussiones Mathematicae. Graph Theory
%D 2017
%P 29-37
%V 37
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2017_37_1_a2/
%G en
%F DMGT_2017_37_1_a2
Flandrin, Evelyne; Li, Hao; Marczyk, Antoni; Saclé, Jean-François; Woźniak, Mariusz. A Note on Neighbor Expanded Sum Distinguishing Index. Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 1, pp. 29-37. http://geodesic.mathdoc.fr/item/DMGT_2017_37_1_a2/

[1] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (Macmillan, London, 1976).

[2] M. Kalkowski, A Note on the 1, 2-Conjecture (Ph. D. Thesis, Adam Mickiewicz University in Pozna’n, 2010).

[3] M. Kalkowski, M. Karoński and F. Pfender, Vertex-coloring edge-weightings: Towards the 1-2-3 -Conjecture, J. Combin. Theory Ser. B 100 (2010) 347–349. doi:10.1016/j.jctb.2009.06.002

[4] M. Karoński, T. Luczak and A. Thomason, Edge weights and vertex colours, J. Combin. Theory Ser. B 91 (2004) 151–157. doi:10.1016/j.jctb.2003.12.001

[5] J. Przyby lo and M. Woźniak, On a 1, 2 Conjecture, Discrete Math. Theor. Comput. Sci. 12 (2010) 101–108.