Distinguishing chromatic number of random Cayley graphs
نویسندگان
چکیده
منابع مشابه
The chromatic number of random Cayley graphs
We consider the typical behaviour of the chromatic number of a random Cayley graph of a given group of order n with respect to a randomly chosen set of size k ≤ n/2. This behaviour depends on the group: for some groups it is typically 2 for all k < 0.99 log2 n, whereas for some other groups it grows whenever k grows. The results obtained include a proof that for any large prime p, and any 1 ≤ k...
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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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Let G be a connected graph. Let f be a proper k -coloring of G and Π = (R_1, R_2, . . . , R_k) bean ordered partition of V (G) into color classes. For any vertex v of G, define the color code c_Π(v) of v with respect to Π to be a k -tuple (d(v, R_1), d(v, R_2), . . . , d(v, R_k)), where d(v, R_i) is the min{d(v, x)|x ∈ R_i}. If distinct vertices have distinct color codes, then we call f a locat...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2017
ISSN: 0012-365X
DOI: 10.1016/j.disc.2017.06.002