Cartesian powers of graphs can be distinguished by two labels
نویسندگان
چکیده
1 The distinguishing number D(G) of a graph G is the least integer d such that there is a d-labeling 2 of the vertices of G which is not preserved by any nontrivial automorphism. For a graph G let Gr 3 be the r th power of G with respect to the Cartesian product. It is proved that D(Gr ) = 2 for any 4 connected graph G with at least 3 vertices and for any r ≥ 3. This confirms and strengthens a 5 conjecture of Albertson. Other graph products are also considered and a refinement of the Russell 6 and Sundaram motion lemma is proved. 7 © 2005 Published by Elsevier Ltd 8
منابع مشابه
Cartesian powers of graphs can be distinguished with two labels
The distinguishing number D(G) of a graph G is the least integer d such that there is a d-labeling of the vertices of G which is not preserved by any nontrivial automorphism. For a graph G let G be the rth power of G with respect to the Cartesian product. It is proved that D(G) = 2 for any connected graph G with at least 3 vertices and for any r ≥ 3. This confirms and strengthens a conjecture o...
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ورودعنوان ژورنال:
- Eur. J. Comb.
دوره 28 شماره
صفحات -
تاریخ انتشار 2007