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

Mariusz Grech

Abstract


In the paper Graphical complexity of products of permutation groups, M. Grech, A. Jeż, and 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 settled for the edge-colored digraphs.

Keywords


Colored graph, automorphism group, permutation group, direct product

Full Text:

PDF


DOI: https://doi.org/10.26493/1855-3974.1926.6ad

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications