منابع مشابه
Distinguishing number and distinguishing index of natural and fractional powers of graphs
The distinguishing number (resp. index) $D(G)$ ($D'(G)$) of a graph $G$ is the least integer $d$ such that $G$ has an vertex labeling (resp. edge labeling) with $d$ labels that is preserved only by a trivial automorphism. For any $n in mathbb{N}$, the $n$-subdivision of $G$ is a simple graph $G^{frac{1}{n}}$ which is constructed by replacing each edge of $G$ with a path of length $n$...
متن کاملDistinguishing Infinite Graphs
The distinguishing number D(G) of a graph G is the least cardinal number א such that G has a labeling with א labels that is only preserved by the trivial automorphism. We show that the distinguishing number of the countable random graph is two, that tree-like graphs with not more than continuum many vertices have distinguishing number two, and determine the distinguishing number of many classes...
متن کاملDistinguishing geometric graphs
We begin the study of distinguishing geometric graphs. Let G be a geometric graph. An automorphism of the underlying graph that preserves both crossings and noncrossings is called a geometric automorphism. A labelling, f : V (G) → {1, 2, . . . , r}, is said to be rdistinguishing if no nontrivial geometric automorphism preserves the labels. The distinguishing number of G is the minimum r such th...
متن کاملList-Distinguishing Colorings of Graphs
A coloring of the vertices of a graph G is said to be distinguishing provided that no nontrivial automorphism of G preserves all of the vertex colors. The distinguishing number of G, denoted D(G), is the minimum number of colors in a distinguishing coloring of G. The distinguishing number, first introduced by Albertson and Collins in 1996, has been widely studied and a number of interesting res...
متن کاملDistinguishing Cartesian powers of graphs
The distinguishing number D(G) of a graph is the least integer d such that there is a d-labeling of the vertices of G that is not preserved by any nontrivial automorphism of G. We show that the distinguishing number of the square and higher powers of a connected graph G 6= K2,K3 with respect to the Cartesian product is 2. This result strengthens results of Albertson [1] on powers of prime graph...
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ژورنال
عنوان ژورنال: Journal of Information and Optimization Sciences
سال: 2020
ISSN: 0252-2667,2169-0103
DOI: 10.1080/02522667.2020.1773614