# Edge-Transitive Lexicographic and Cartesian Products

• Volume: 36, Issue: 4, page 857-865
• ISSN: 2083-5892

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## Abstract

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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.

## How to cite

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Wilfried Imrich, et al. "Edge-Transitive Lexicographic and Cartesian Products." Discussiones Mathematicae Graph Theory 36.4 (2016): 857-865. <http://eudml.org/doc/287124>.

@article{WilfriedImrich2016,
abstract = {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.},
author = {Wilfried Imrich, Ali Iranmanesh, Sandi Klavžar, Abolghasem Soltani},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {edge-transitive graph; vertex-transitive graph; lexicographic product of graphs; Cartesian product of graphs},
language = {eng},
number = {4},
pages = {857-865},
title = {Edge-Transitive Lexicographic and Cartesian Products},
url = {http://eudml.org/doc/287124},
volume = {36},
year = {2016},
}

TY - JOUR
AU - Wilfried Imrich
AU - Ali Iranmanesh
AU - Sandi Klavžar
AU - Abolghasem Soltani
TI - Edge-Transitive Lexicographic and Cartesian Products
JO - Discussiones Mathematicae Graph Theory
PY - 2016
VL - 36
IS - 4
SP - 857
EP - 865
AB - 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.
LA - eng
KW - edge-transitive graph; vertex-transitive graph; lexicographic product of graphs; Cartesian product of graphs
UR - http://eudml.org/doc/287124
ER -

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