The distinguishing number and distinguishing index of the lexicographic product of two graphs
نویسندگان
چکیده
منابع مشابه
The relationship between the distinguishing number and the distinguishing index with detection number of a graph
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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 $n$...
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The distinguishing number $D(G)$ of a graph $G$ is the least integer $d$ such that $G$ has a vertex labeling with $d$ labels that is preserved only by a trivial automorphism. The distinguishing chromatic number $chi_{D}(G)$ of $G$ is defined similarly, where, in addition, $f$ is assumed to be a proper labeling. We prove that if $G$ is a bipartite graph of girth at least six with the maximum ...
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15 صفحه اولThe Distinguishing Index of Infinite Graphs
The distinguishing index D′(G) of a graph G is the least cardinal d such that G has an edge colouring with d colours that is only preserved by the trivial automorphism. This is similar to the notion of the distinguishing number D(G) of a graph G, which is defined with respect to vertex colourings. We derive several bounds for infinite graphs, in particular, we prove the general bound D′(G) 6 ∆(...
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2018
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.2070