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The determining number of a Cartesian product
Journal of Graph Theory, 2009AbstractA set S of vertices is a determining set for a graph G if every automorphism of G is uniquely determined by its action on S. The determining number of G, denoted Det(G), is the size of a smallest determining set. This paper begins by proving that if G=G□⋅□G is the prime factor decomposition of a connected graph then Det(G)=max{Det(G)}.
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The general position number of Cartesian products involving a factor with small diameter
Applied Mathematics and Computation, 2021Kexiang Xu
exaly
Italian domination of Cartesian products of directed cycles
Discrete Applied Mathematics, 2021Christopher M van Bommel
exaly
Domination in digraphs and their direct and Cartesian products
Journal of Graph Theory, 2022Boštjan Brešar +2 more
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