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Distinguishing Chromatic Number of Cartesian Products of Graphs

✍ Scribed by Choi, Jeong Ok; Hartke, Stephen G.; Kaul, Hemanshu

Book ID
118196930
Publisher
Society for Industrial and Applied Mathematics
Year
2010
Tongue
English
Weight
282 KB
Volume
24
Category
Article
ISSN
0895-4801

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## Abstract The __circular chromatic index__ of a graph __G__, written $\chi\_{c}'(G)$, is the minimum __r__ permitting a function $f : E(G)\rightarrow [0,r)$ such that $1 \le | f(e)-f(e')|\le r - 1$ whenever __e__ and $e'$ are incident. Let $G = H$ β–‘ $C\_{2m +1}$, where β–‘ denotes Cartesian product

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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 = K 2 , K 3 with respect to t