The Cartesian product of graphs with loops
Boiko, Tetiana ; Cuno, Johannes ; Imrich, Wilfried ; Lehner, Florian ; van de Woestijne, Christiaan E.
ARS MATHEMATICA CONTEMPORANEA, Tome 11 (2015), / Harvested from ARS MATHEMATICA CONTEMPORANEA
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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.

Publié le : 2015-01-01
DOI : https://doi.org/10.26493/1855-3974.715.c3d 
@article{715,
     title = {The Cartesian product of graphs with loops},
     journal = {ARS MATHEMATICA CONTEMPORANEA},
     volume = {11},
     year = {2015},
     doi = {10.26493/1855-3974.715.c3d},
     language = {EN},
     url = {http://dml.mathdoc.fr/item/715}
}

Boiko, Tetiana; Cuno, Johannes; Imrich, Wilfried; Lehner, Florian; van de Woestijne, Christiaan E. The Cartesian product of graphs with loops. ARS MATHEMATICA CONTEMPORANEA, Tome 11 (2015) . doi : 10.26493/1855-3974.715.c3d. http://gdmltest.u-ga.fr/item/715/