The independence polynomial of n-th central graph of dihedral groups
Keywords: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.
Balakrishnan, P., Sattanathan, M., Kala, R. 2011. The center graph of a group. South Asian Journal of Mathematics. 1(1), 21-28.
Balakrishnan, R. and Ranganathan, K. 2012. A textbook of graph theory, 2nd ed. New York: Springer.
Bertram, E. A. 1983. Some applications of graph theory to finite groups. Discrete Mathematics. 44, 31-43.
Ferrin, G. 2014. Independence Polynomials, Master Dissertation.
Fraleigh, J. B. 2003. A first course in abstract algebra, 7th ed. U.S.A.: Pearson Education, Inc.
Hoede, C. and Li, X. 1994. Clique polynomials and independent set polynomials of graphs. Discrete Mathematics. 125, 219-228.
Karimi, Z., Erfanian, A., Tolue, B. 2016. n-th central graph of a group. Comptes rendus de l’Acade'mie bulgare des Sciences. 69, 135-144.
Levit, V. E. and E. Mandrescu. 2005. The Independence Polynomial of a Graph – A Survey. Proceedings of the 1st International Conference on Algebraic Informatics. Aristotle Univ.
Thessaloniki. 3 October 2005. Thessaloniki. 233254.
Rose, H. E. 2009. A course on finite groups. London: Springer-Verlag.
Rosen, K. H. 2013. Discrete mathematics and its applications, 7th ed. New York: McGraw-Hill.
Rotman, J. J. 2003. Advanced modern algebra. USA: Prentice Hall.