Balachandran, Niranjan and Padinhatteeri, Sajith and Spiga, Pablo (2019) Vertex transitive graphs G with χD(G) > χ(G) and small automorphism group. In: ARS MATHEMATICA CONTEMPORANEA, 17 (1). pp. 311-318.
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Abstract
For a graph G and a positive integer k, a vertex labelling f : V (G) -> {1, 2,...,k} is said to be k-distinguishing if no non-trivial automorphism of G preserves the sets f(-1) (i) for each i epsilon {1,...,k}. The distinguishing chromatic number of a graph G, denoted chi(D)(G), is defined as the minimum k such that there is a k-distinguishing labelling of V (G) which is also a proper coloring of the vertices of G. In this paper, we prove the following theorem: Given k epsilon N, there exists an infinite sequence of vertex-transitive graphs G(i) = (V-i, E-i) such that 1. chi(D)(G(i)) > chi(G(i)) > k, 2. vertical bar Aut(G(i))vertical bar < 2k vertical bar V-i vertical bar, where Aut(G(i)) denotes the full automorphism group of G(i). In particular, this answers a question posed by the first and second authors of this paper.
| Item Type: | Journal Article |
|---|---|
| Publication: | ARS MATHEMATICA CONTEMPORANEA |
| Publisher: | UP FAMNIT |
| Additional Information: | Copyright of this article belongs to UP FAMNIT |
| Keywords: | Distinguishing chromatic number; vertex transitive graphs; Cayley graphs |
| Department/Centre: | Division of Electrical Sciences > Electrical Communication Engineering |
| Date Deposited: | 29 Nov 2019 06:52 |
| Last Modified: | 26 Aug 2022 09:41 |
| URI: | https://eprints.iisc.ac.in/id/eprint/64021 |
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