Abstract
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.
Keywords: vertex coloring, distinguishing number, automorphisms, infinite
graphs, Cartesian and weak Cartesian product.
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.
Keywords: vertex coloring, distinguishing number, automorphisms, infinite
graphs, Cartesian and weak Cartesian product.
| Original language | English |
|---|---|
| Pages (from-to) | 155-164 |
| Number of pages | 10 |
| Journal | Discussiones mathematicae / Graph theory |
| Volume | 37.2017 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Dec 2017 |