Abstract
A vertex coloring of a graph G is distinguishing if non-identity automorphisms do not preserve it. The distinguishing number, D(G), is the minimum number of colors required for such a coloring and the distinguishing threshold, \(\theta (G)\), is the minimum number of colors k such that any arbitrary k-coloring is distinguishing. Moreover, \(\Phi _k (G)\) is the number of distinguishing coloring of G using at most k colors. In this paper, for some graph operations, namely, vertex-sum, rooted product, corona product and lexicographic product, we find formulae of the distinguishing number and threshold using \(\Phi _k (G)\).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
