Destroying automorphisms by fixing nodes
نویسندگان
چکیده
The fixing number of a graph G is the minimum cardinality of a set S ⊂ V (G) such that every nonidentity automorphism of G moves at least one member of S, i.e., the automorphism group of the graph obtained from G by fixing every node in S is trivial. We provide a formula for the fixing number of a disconnected graph in terms of the fixing numbers of its components and make some observations about graphs with small fixing numbers. We determine the fixing number of a tree and find a necessary and sufficient condition for a tree to have fixing number 1. © 2006 Elsevier B.V. All rights reserved.
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 306 شماره
صفحات -
تاریخ انتشار 2006