Abstract
An independent dominating set of a graph is a vertex subset that is both dominating and independent set in the graph, i.e., a maximal independent set. Also, the independent domination polynomial is an ordinary generating function for the number of independent dominating sets in the graph. In this paper, we examine independent domination polynomials of zero-divisor graphs of the ring \({\mathbb {Z}}_n\) where \(n\in \{2p, p^2, p^\alpha ,pq, p^2q, pqr\}\) and their roots. Finally, we prove the log-concavity and unimodality of their independent domination polynomials.
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The author contributed to the study conception, design. Material preparation, data collection, and analysis were performed by Necla Kırcalı Gürsoy, Alper Ülker, and Arif Gürsoy. The authors read and approved the final manuscript.
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Kırcalı Gürsoy, N., Ülker, A. & Gürsoy, A. Independent domination polynomial of zero-divisor graphs of commutative rings. Soft Comput 26, 6989–6997 (2022). https://doi.org/10.1007/s00500-022-07217-2
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DOI: https://doi.org/10.1007/s00500-022-07217-2