Distinguishing number and distinguishing index of some operations on graphs
نویسندگان
چکیده
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 $n$...
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Introduced by Albertson and al. [1], the distinguishing number D(G) of a graph G is the least integer r such that there is a r-labeling of the vertices of G that is not preserved by any nontrivial automorphism of G. Most of graphs studied in literature have 2 as a distinguishing number value except complete, multipartite graphs or cartesian product of complete graphs not depend on n. In this pa...
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A proper edge colouring of a graph G without isolated edges is neighbour-distinguishing if any two adjacent vertices have distinct sets consisting of colours of their incident edges. The neighbour-distinguishing index of G is the minimum number ndi(G) of colours in a neighbour-distinguishing edge colouring of G. According to a conjecture by Zhang, Liu and Wang (2002), ndi(G) ≤ ∆(G) + 2 provided...
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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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ژورنال
عنوان ژورنال: Journal of Information and Optimization Sciences
سال: 2018
ISSN: 0252-2667,2169-0103
DOI: 10.1080/02522667.2017.1294304