# Edge-Transitive Lexicographic and Cartesian Products

Wilfried Imrich; Ali Iranmanesh; Sandi Klavžar; Abolghasem Soltani

Discussiones Mathematicae Graph Theory (2016)

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

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topWilfried 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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