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. 311318.

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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 kdistinguishing if no nontrivial 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 kdistinguishing 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 vertextransitive graphs G(i) = (Vi, Ei) such that 1. chi(D)(G(i)) > chi(G(i)) > k, 2. vertical bar Aut(G(i))vertical bar < 2k vertical bar Vi 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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