Geodesic
Edge-Transitive Lexicographic and Cartesian Products
Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 4, pp. 857-865

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

In this note connected, edge-transitive lexicographic and Cartesian products are characterized. For the lexicographic product G ◦ H of a connected graph G that is not complete by a graph H, we show that it is edge-transitive if and only if G is edge-transitive and H is edgeless. If the first factor of G ∘ H is non-trivial and complete, then G ∘ H is edge-transitive if and only if H is the lexicographic product of a complete graph by an edgeless graph. This fixes an error of Li, Wang, Xu, and Zhao [11]. For the Cartesian product it is shown that every connected Cartesian product of at least two non-trivial factors is edge-transitive if and only if it is the Cartesian power of a connected, edge- and vertex-transitive graph.
Keywords: edge-transitive graph, vertex-transitive graph, lexicographic product of graphs, Cartesian product of graphs 
@article{DMGT_2016_36_4_a6,
     author = {Imrich, Wilfried and Iranmanesh, Ali and Klav\v{z}ar, Sandi and Soltani, Abolghasem},
     title = {Edge-Transitive {Lexicographic} and {Cartesian} {Products}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {857--865},
     publisher = {mathdoc},
     volume = {36},
     number = {4},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2016_36_4_a6/}
}
TY  - JOUR
AU  - Imrich, Wilfried
AU  - Iranmanesh, Ali
AU  - Klavžar, Sandi
AU  - Soltani, Abolghasem
TI  - Edge-Transitive Lexicographic and Cartesian Products
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2016
SP  - 857
EP  - 865
VL  - 36
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2016_36_4_a6/
LA  - en
ID  - DMGT_2016_36_4_a6
ER  - 
%0 Journal Article
%A Imrich, Wilfried
%A Iranmanesh, Ali
%A Klavžar, Sandi
%A Soltani, Abolghasem
%T Edge-Transitive Lexicographic and Cartesian Products
%J Discussiones Mathematicae. Graph Theory
%D 2016
%P 857-865
%V 36
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2016_36_4_a6/
%G en
%F DMGT_2016_36_4_a6
Imrich, Wilfried; Iranmanesh, Ali; Klavžar, Sandi; Soltani, Abolghasem. Edge-Transitive Lexicographic and Cartesian Products. Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 4, pp. 857-865. http://geodesic.mathdoc.fr/item/DMGT_2016_36_4_a6/