Zobrazeno 1 - 10
of 179
pro vyhledávání: '"Imrich, Wilfried"'
In this note, we extend results about unique $n^{\textrm{th}}$ roots and cancellation of finite disconnected graphs with respect to the Cartesian, the strong and the direct product, to the rooted hierarchical products, and to a modified lexicographic
Externí odkaz:
http://arxiv.org/abs/2407.02615
A graph $G$ is asymmetrizable if it has a set of vertices whose setwise stablizer only consists of the identity automorphism. The motion $m$ of a graph is the minimum number of vertices moved by any non-identity automorphism. It is known that infinit
Externí odkaz:
http://arxiv.org/abs/2301.10380
Autor:
Imrich, Wilfried, Stadler, Peter F.
We introduce the concept of neighborhood systems as a generalization of directed, reflexive graphs and show that the prime factorization of neighborhood systems with respect to the the direct product is unique under the condition that they satisfy an
Externí odkaz:
https://ul.qucosa.de/id/qucosa%3A33060
https://ul.qucosa.de/api/qucosa%3A33060/attachment/ATT-0/
https://ul.qucosa.de/api/qucosa%3A33060/attachment/ATT-0/
Publikováno v:
The electronic journal of combinatorics 24(3) (2017), #P3.6
We consider infinite graphs. The distinguishing number $D(G)$ of a graph $G$ is the minimum number of colours in a vertex colouring of $G$ that is preserved only by the trivial automorphism. An analogous invariant for edge colourings is called the di
Externí odkaz:
http://arxiv.org/abs/1910.12107
The distinguishing number $D(G)$ of a graph $G$ is the smallest number of colors that is needed to color the vertices of $G$ such that the only color preserving automorphism is the identity. For infinite graphs $D(G)$ is bounded by the supremum of th
Externí odkaz:
http://arxiv.org/abs/1810.02265
If a graph $G$ has distinguishing number 2, then there exists a partition of its vertex set into two parts, such that no nontrivial automorphism of $G$ fixes setwise the two parts. Such a partition is called a 2-distinguishing coloring of $G$, and th
Externí odkaz:
http://arxiv.org/abs/1801.02405
The distinguishing number $D(G)$ of a graph $G$ is the smallest number of colors that is needed to color $G$ such that the only color preserving automorphism is the identity. We give a complete classification for all connected graphs $G$ of maximum v
Externí odkaz:
http://arxiv.org/abs/1709.05797
The practical application of graph prime factorization algorithms is limited in practice by unavoidable noise in the data. A first step towards error-tolerant "approximate" prime factorization, is the development of local approaches that cover the gr
Externí odkaz:
http://arxiv.org/abs/1705.03823
Autor:
Imrich, Wilfried, Peterin, Iztok
We show that every nontrivial finite or infinite connected directed graph with loops and at least one vertex without a loop is uniquely representable as a Cartesian or weak Cartesian product of prime graphs. For finite graphs the factorization can be
Externí odkaz:
http://arxiv.org/abs/1702.05946