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Radicals commuting with cartesian products
Archiv der Mathematik, 1998Given an Abelian group \(G\), the group radical is defined by \(R_G(X)=\bigcap\{\text{Ker }\phi\mid\phi\colon X\to G\}\), for Abelian groups \(X\). This radical does not always commute with infinite direct products (for instance, when \(G=\mathbb{Q}\), it turns into the torsion radical).
Corner, A. L. S., Göbel, Rüdiger
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Factoring cartesian‐product graphs
Journal of Graph Theory, 1994AbstractIn a fundamental paper, G. Sabidussi [“Graph Multiplication,” Mathematische Zeitschrift, Vol. 72 (1960), pp. 446–457] used a tower of equivalence relations on the edge set E(G) of a connected graph G to decompose G into a Cartesian product of prime graphs. Later, a method by R.L. Graham and P.M.
Imrich, Wilfried, Žerovnik, Janez
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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
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Controllability of Cartesian Product Signed Networks
IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2023Junjie Huang, Housheng Su
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