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Edge-transitive lexicographic and cartesian products
Wilfried Imrich, Ali Iranmanesh, Sandi Klavžar, Abolghasem Soltani, 2016, izvirni znanstveni članek

Opis: In 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.
Ključne besede: edge-transitive graph, vertex-transitive graph, lexicographic product of graphs, Cartesian product of graphs
Objavljeno: 31.03.2017; Ogledov: 597; Prenosov: 351
.pdf Celotno besedilo (150,33 KB)
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