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Vertex transitive graphs G with χD(G) > χ(G) and small automorphism group

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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Official URL: http://dx.doi.org/10.26493/1855-3974.1435.c71


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
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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