Edge-transitive lexicographic and Cartesian products | Zendy

Wilfried Imrich | Zendy; Ali Iranmanesh | Zendy; Sandi Klavžar | Zendy; Abolghasem Soltani | Zendy

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Edge-transitive lexicographic and Cartesian products

Author(s) -

Wilfried Imrich,

Ali Iranmanesh,

Sandi Klavžar,

Abolghasem Soltani

Publication year - 2016

Publication title -

discussiones mathematicae graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.476

H-Index - 19

eISSN - 2083-5892

pISSN - 1234-3099

DOI - 10.7151/dmgt.1892

Subject(s) - cartesian product , lexicographical order , transitive relation , mathematics , transitive reduction , combinatorics , transitive closure , vertex (graph theory) , graph , cartesian coordinate system , graph product , discrete mathematics , voltage graph , chordal graph , line graph , geometry , 1 planar graph

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

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