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Title: Dominating Sets and Domination Polynomials of Stars
Authors: Sahib Shayyal Kahat; Abdul Jalil M. Khalaf; Roslan Hasni
DOI:
Aff: Department of Mathematics, Faculty of Mathematics and Computer Science, University of Kufa, P.O. Box 21, Najaf, IRAQ.
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Keywords: Dominating Sets; Domination Polynomials; Domination Number
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Abstract:Background: Let .. = (..,..)be a simple graph. .. set..... is a dominating set of.., if every vertex in ..-..is adjacent to at least one vertex in ... Let Snbe star graph with order n. LetSni be the family of dominating sets of a star Snwith cardinality .., and let .. ....,.. = ...... . Results. In this paper, we construct ...., and obtain a recursive formula for .. ....,.. . Conclusion. Using this recursive formula, we consider the polynomial .. ....,.. = .. ....,.. ........=1, which we call domination polynomial of star graphs and obtain some properties of this polynomial