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Distinguishing Threshold for Some Graph Operations

机译：Distinguishing Threshold for Some Graph Operations

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摘要

A vertex coloring of a graph G is distinguishing if non-identity automorphisms do not preserve it. The distinguishing number, D(G), is the minimum number of colors required for such a coloring and the distinguishing threshold, 8(G), is the minimum number of colors k such that any arbitrary k-coloring is distinguishing. Moreover, Φ_K(G) is the number of distinguishing coloring of G using at most k colors. In this paper, for some graph operations, namely, vertex-sum, rooted product, corona product and lexicographic product, we find formulae of the distinguishing number and threshold using Φ_k(G).

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