Edge-transitive lexicographic and cartesian productsImrich, Wilfried (Avtor) Iranmanesh, Ali (Avtor) Klavžar, Sandi (Avtor) Soltani, Abolghasem (Avtor) edge-transitive graphvertex-transitive graphlexicographic product of graphsCartesian product of graphsIn this note connected, edge-transitive lexicographic and Cartesian products are characterized. For the lexicographic product ▫$G \circ H$▫ 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 ▫$G \circ H$▫ is non-trivial and complete, then ▫$G \circ H$▫ 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 (Appl. Math. Lett. 24 (2011) 1924--1926). 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.University of Zielona Góra20162017-03-31 11:06:16Znanstveno delo65337ISSN: 1234-3099UDK: 519.17OceCobissID: 7487065COBISS_ID: 17777241ISSN pri članku: 1234-3099NUK URN: URN:SI:UM:DK:HWK1G8VHsl