Decompositions of the authomorphism groups of edge-colored graphs into the direct product of permutation groups

2019/03/18 by Mariusz Grech, Grech, Mariusz
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1903.07419

arxiv created 2019/03/18 · arxiv updated 2019/03/19

Abstract

In the paper Graphical complexity of products of permutation groups, M. Grech, A. Jez, A. Kisielewicz have proved that the direct product of automorphism groups of edge-colored graphs is itself the automorphism groups of an edge-colored graph. In this paper, we study the direct product of two permutation groups such that at least one of them fails to be the automorphism group of an edge-colored graph. We find necessary and sufficient conditions for the direct product to be the automorphism group of an edge-colored graph. The same problem is solved for the edge-colored digraphs.

Related

• Wreath product in automorphism groups of graphs
• Graphical Cyclic Permutation Groups
• Complete Edge-Colored Permutation Graphs
• Colour-permuting automorphisms of complete Cayley graphs
• Isomorphisms and automorphisms of graph products of groups