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In a given graph G, a set S of vertices with an assignment of colours to them is a defining set of the vertex colouring of G, if there exists a unique extension of the colours of S to a χ(G)-colouring of the vertices of G.A defining set with minimum cardinality is called a minimum defining set (of vertex colouring) and its cardinality, the defining number, is denoted by d(G, χ). Mahmoodian et al...
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