Geodesic
The Cartesian product of graphs with loops
Ars Mathematica Contemporanea, Tome 11 (2016) no. 1, pp. 1-9.

Voir la notice de l'article provenant de la source Ars Mathematica Contemporanea website

We extend the definition of the Cartesian product to graphs with loops and show that the Sabidussi–Vizing unique factorization theorem for connected finite simple graphs still holds in this context for all connected finite graphs with at least one unlooped vertex. We also prove that this factorization can be computed in O(m) time, where m is the number of edges of the given graph.
DOI : 10.26493/1855-3974.715.c3d
Keywords: Graphs, monoids, factorizations, algorithms. 
@article{10_26493_1855_3974_715_c3d,
     author = {Tetiana Boiko and Johannes Cuno and Wilfried Imrich and Florian Lehner and Christiaan E. van de Woestijne},
     title = {The {Cartesian} product of graphs with loops},
     journal = {Ars Mathematica Contemporanea},
     pages = {1--9},
     publisher = {mathdoc},
     volume = {11},
     number = {1},
     year = {2016},
     doi = {10.26493/1855-3974.715.c3d},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.715.c3d/}
}
TY  - JOUR
AU  - Tetiana Boiko
AU  - Johannes Cuno
AU  - Wilfried Imrich
AU  - Florian Lehner
AU  - Christiaan E. van de Woestijne
TI  - The Cartesian product of graphs with loops
JO  - Ars Mathematica Contemporanea
PY  - 2016
SP  - 1
EP  - 9
VL  - 11
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.715.c3d/
DO  - 10.26493/1855-3974.715.c3d
LA  - en
ID  - 10_26493_1855_3974_715_c3d
ER  - 
%0 Journal Article
%A Tetiana Boiko
%A Johannes Cuno
%A Wilfried Imrich
%A Florian Lehner
%A Christiaan E. van de Woestijne
%T The Cartesian product of graphs with loops
%J Ars Mathematica Contemporanea
%D 2016
%P 1-9
%V 11
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.715.c3d/
%R 10.26493/1855-3974.715.c3d
%G en
%F 10_26493_1855_3974_715_c3d
Tetiana Boiko; Johannes Cuno; Wilfried Imrich; Florian Lehner; Christiaan E. van de Woestijne. The Cartesian product of graphs with loops. Ars Mathematica Contemporanea, Tome 11 (2016) no. 1, pp. 1-9. doi : 10.26493/1855-3974.715.c3d. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.715.c3d/

Cité par Sources :