Geodesic
Decompositions of the automorphism groups of edge-colored graphs into the direct product of permutation groups
Ars mathematica contemporanea, Tome 21 (2021) no. 2, article no. 06, 11 p. Cet article a éte moissonné depuis la source Ars Mathematica Contemporanea website

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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.
DOI : 10.26493/1855-3974.1926.6ad
Keywords: Colored graph, automorphism group, permutation group, direct product 
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	},
     journal = {Ars mathematica contemporanea},
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Mariusz Grech. Decompositions of the automorphism groups of edge-colored graphs into the direct product of permutation groups. Ars mathematica contemporanea, Tome 21 (2021) no. 2, article  no. 06, 11 p.. doi: 10.26493/1855-3974.1926.6ad

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