The independence polynomial of n-th central graph of dihedral groups


  • Nabilah Najmuddin Universiti Teknologi Malaysia
  • Nor Haniza Sarmin Universiti Teknologi Malaysia
  • Ahmad Erfanian Ferdowsi University of Mashhad
  • Hamisan Rahmat Universiti Teknologi Malaysia



Independence polynomial, n-th central graph, dihedral group


An independent set of a graph is a set of pairwise non-adjacent vertices while the independence number is the maximum cardinality of an independent set in the graph. The independence polynomial of a graph is defined as a polynomial in which the coefficient is the number of the independent set in the graph.  Meanwhile, a graph of a group G is called n-th central if the vertices are elements of G and two distinct vertices are adjacent if they are elements in the n-th term of the upper central series of G. In this research, the independence polynomial of the n-th central graph is found for some dihedral groups.

Author Biographies

Nabilah Najmuddin, Universiti Teknologi Malaysia

Candidate, Doctor of Philosophy (Mathematics)Department of Mathematical Sciences,Faculty of Science,Universiti Teknologi Malaysia

Nor Haniza Sarmin, Universiti Teknologi Malaysia

Professor of Mathematics,

Department of Mathematical Sciences,Faculty of Science,Universiti Teknologi Malaysia

Ahmad Erfanian, Ferdowsi University of Mashhad

Ferdowsi University of Mashhad


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