Edge-Transitive Lexicographic and Cartesian Products

• Autorzy: Wilfried Imrich , Ali Iranmanesh , Sandi Klavžar , Abolghasem Soltani
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

edge-transitive graph; vertex-transitive graph; lexicographic product of graphs; Cartesian product of graphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2016
• Tom: 36
• Numer: 4
• Strony: 857-865

Daty

wydano

2016-11-01

otrzymano

2015-04-16

poprawiono

2015-12-29

zaakceptowano

2015-12-29

online

2016-10-21

Twórcy

autor

Wilfried Imrich

• Montanuniversität Leoben, Leoben,

autor

Ali Iranmanesh

• Department of Mathematics, University of Tarbiat Modares, Tehran,

autor

Sandi Klavžar

• Faculty of Mathematics and Physics, University of Ljubljana, Slovenia
• Faculty of Natural Sciences and Mathematics, University of Maribor, Slovenia
• Institute of Mathematics, Physics and Mechanics, Ljubljana,

autor

Abolghasem Soltani

• Department of Mathematics, University of Tarbiat Modares, Tehran,

Identyfikatory

DOI

10.7151/dmgt.1892