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Destroying symmetry by orienting edges: complete graphs and complete bigraphs

Frank Harary, Michael S. Jacobson (2001)

Discussiones Mathematicae Graph Theory

Our purpose is to introduce the concept of determining the smallest number of edges of a graph which can be oriented so that the resulting mixed graph has the trivial automorphism group. We find that this number for complete graphs is related to the number of identity oriented trees. For complete bipartite graphs K s , t , s ≤ t, this number does not always exist. We determine for s ≤ 4 the values of t for which this number does exist.

Distinguishing Cartesian Products of Countable Graphs

Ehsan Estaji, Wilfried Imrich, Rafał Kalinowski, Monika Pilśniak, Thomas Tucker (2017)

Discussiones Mathematicae Graph Theory

The distinguishing number D(G) of a graph G is the minimum number of colors needed to color the vertices of G such that the coloring is preserved only by the trivial automorphism. In this paper we improve results about the distinguishing number of Cartesian products of finite and infinite graphs by removing restrictions to prime or relatively prime factors.

Dynamic cage survey.

Exoo, Geoffrey, Jajcay, Robert (2008)

The Electronic Journal of Combinatorics [electronic only]

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